Math Tutorials

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Do you need math help in reviewing key topics in algebra by way of worked-out examples? Are you limited by the math examples in your textbook?

Here we provide hundreds of math tutorials from key topics in algebra. From the slope formula, to the quadratic formula, to algebra tiles and logarithms, you will find a wealth of material. Use these math tutorials as brief reviews or homework help to supplement your textbook materials.

Each math tutorial launches a new page, which you can then print or display on your whiteboard. We also include quizzes for many of the math concepts.

Math Tutorials

• Algebra Tiles
• Solving Equations in One Variable
• Solving Equations with Fractions
• Solving Equations with Percents
• Slope formula
• Midpoint formula
• Distance formula
• Linear functions, given m and b
• Absolute value functions
• Linear inequalities
• Point-Slope form
• Equation of a line given two points
• Graphing parallel and perpendicular lines
• Solving quadratics graphically

• Solving Equations by Completing the square
• Factoring Quadratics
• Polynomial Expansion
• Solving Equations with the Quadratic formula
• FOIL
• Exponential Functions
• Laws of Exponents
• Logarithmic Functions
• Rational Functions
• Rational Expressions
• Conic Sections

Math Tutorials: Algebra Tiles

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Addition. Calculating a + b using algebra tiles, under the following conditions:

• Math Tutorial 1: a > 0, b > 0, sum is positive
• Math Tutorial 2: a > 0, b < 0, sum is positive
• Math Tutorial 3: a > 0, b < 0, sum is negative
• Math Tutorial 4: a > 0, b < 0, sum is zero
• Math Tutorial 5: a < 0, b < 0, sum is negative

Subtraction. Calculating a – b using algebra tiles, under the following conditions:

1. Math Tutorial 6: a > 0, b > 0, difference is positive
2. Math Tutorial 7: a > 0, b > 0, difference is negative
3. Math Tutorial 8: a > 0, b > 0, difference is zero
4. Math Tutorial 9: a > 0, b < 0, difference is positive
5. Math Tutorial 10: a < 0, b > 0, difference is negative
6. Math Tutorial 11: a < 0, b < 0, difference is negative
7. Math Tutorial 12: a < 0, b < 0, difference is positive
8. Math Tutorial 13: a < 0, b < 0, difference is zero

Solving Linear Equations.

Solving x + a = b using algebra tiles, under the following conditions:

1. Math Tutorial 14: a > 0, b > 0, solution is positive
2. Math Tutorial 15: a > 0, b > 0, solution is negative
3. Math Tutorial 16: a > 0, b > 0, solution is zero
4. Math Tutorial 17: a < 0, b > 0, solution is positive
5. Math Tutorial 18: a > 0, b < 0, solution is positive
6. Math Tutorial 19: a < 0, b < 0, solution is positive
7. Math Tutorial 20: a < 0, b < 0, solution is negative
8. Math Tutorial 21: a < 0, b < 0, solution is zero

Solving ax + b = x + c using algebra tiles, under the following conditions:

• Math Tutorial 22: a > 0, b > 0, c > 0, solution is positive
• Math Tutorial 23: a > 0, b > 0, c > 0, solution is negative
• Math Tutorial 24: a > 0, b > 0, c > 0, solution is zero
• Math Tutorial 25: a > 0, b < 0, c > 0, solution is positive
• Math Tutorial 26: a > 0, b > 0, c < 0, solution is negative
• Math Tutorial 27: a > 0, b < 0, c < 0, solution is positive
• Math Tutorial 28: a > 0, b < 0, c < 0, solution is negative
• Math Tutorial 29: a > 0, b < 0, c < 0, solution is zero

Solving Quadratic Equations.

Solving ax² + bx + c = 0 using algebra tiles, under the following conditions:

1. Math Tutorial 30: a > 0, b > 0, c < 0, one real root
2. Math Tutorial 31: a > 0, b > 0, c > 0, one real root
3. Math Tutorial 32: a > 0, b < 0, c > 0, two real roots
4. Math Tutorial 33: a > 0, b < 0, c > 0, two real roots

Subtraction Equations.

Solving x – a = b using algebra tiles, under the following conditions:

1. Math Tutorial 34: a > 0, b > 0, solution is positive
2. Math Tutorial 35: a > 0, b < 0, solution is negative
3. Math Tutorial 36: a > 0, b < 0, solution is zero
4. Math Tutorial 37: a < 0, b > 0, solution is positive
5. Math Tutorial 38: a < 0, b > 0, solution is negative
6. Math Tutorial 39: a < 0, b > 0, solution is zero

Need more math help? See our Math Solvers, which include math tools for algebra.

Math Tutorials: Solving Equations with Fractions in One Variable

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In these examples, solving equations with fractions under the following conditions:

1. Solving Equations, Example 1: a/bx = c
2. Solving Equations, Example 2: -a/bx = c
3. Solving Equations, Example 3: a/bx = -c
4. Solving Equations, Example 4: a/bx = cx + d
5. Solving Equations, Example 5: a/bx = c/dx + e
6. Solving Equations, Example 6: -a/bx = c/dx + e
7. Solving Equations, Example 7: a/bx = -c/dx + e
8. Solving Equations, Example 8: -a/bx = c/dx - e
9. Solving Equations, Example 9: a/bx + c = d/ex + f
10. Solving Equations, Example 10: a/bx - c = d/ex + f
11. Solving Equations, Example 11: a/bx - c = d/ex - f
12. Solving Equations, Example 12: -a/bx + c = -d/ex + f
13. Solving Equations, Example 13: -a/bx + c = d/ex - f

Need more math help? See our Math Solvers, which include math tools for algebra.

Math Tutorials: Solving Equations in One Variable

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In these examples, solving equations under the following conditions:

1. Solving Equations, Example 1: x + a = b
2. Solving Equations, Example 2: x - a = b
3. Solving Equations, Example 3: x + a = -b
4. Solving Equations, Example 4: x - a = -b
5. Solving Equations, Example 5: ax + b = c
6. Solving Equations, Example 6: ax - b = c
7. Solving Equations, Example 7: ax + b = -c
8. Solving Equations, Example 8: -ax + b = c
9. Solving Equations, Example 9: -ax - b = c
10. Solving Equations, Example 10: -ax + b = -c
11. Solving Equations, Example 11: -ax - b = -c
12. Solving Equations, Example 12: ax + b = cx + d
13. Solving Equations, Example 13: ax - b = cx + d
14. Solving Equations, Example 14: ax + b = cx - d
15. Solving Equations, Example 15: ax - b = cx - d
16. Solving Equations, Example 16: ax + b = -cx + d
17. Solving Equations, Example 17: ax - b = -cx + d
18. Solving Equations, Example 18: ax + b = -cx - d
19. Solving Equations, Example 19: ax - b = -cx - d
20. Solving Equations, Example 20: -ax + b = cx + d
21. Solving Equations, Example 21: -ax - b = cx + d
22. Solving Equations, Example 22: -ax + b = -cx + d
23. Solving Equations, Example 23: -ax - b = -cx + d
24. Solving Equations, Example 24: -ax + b = -cx + d
25. Solving Equations, Example 25: -ax + b = -cx - d
26. Solving Equations, Example 26: -ax - b = cx - d
27. Solving Equations, Example 27: -ax - b = -cx - d

Need more math help? See our Math Solvers, which include math tools for algebra.

Math Tutorials: Solving Equations with Percents

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Finding a% of b, under these conditions:

1. Solving Equations, Example 1: 0 < a < 10, 0 < b < 10, b is an integer
2. Solving Equations, Example 2: 0 < a < 10, 0 < b < 10, b is a decimal
3. Solving Equations, Example 3: 0 < a < 10, 10 ≤ b < 100, b is an integer
4. Solving Equations, Example 4: 0 < a < 10, 10 ≤ b < 100, b is an integer
5. Solving Equations, Example 5: 10 ≤ a < 100, 0 < b < 10, b is an integer
6. Solving Equations, Example 6: 10 ≤ a < 100, 0 < b < 10, b is a decimal
7. Solving Equations, Example 7: 10 ≤ a < 100, 10 ≤ b < 100, b is an integer
8. Solving Equations, Example 8: 10 ≤ a < 100, 10 ≤ b < 100, b is a decimal
9. Solving Equations, Example 9: a ≥ 100, 0 < b < 10, b is an integer
10. Solving Equations, Example 10: a ≥ 100, 10 < b < 10, b is a decimal
11. Solving Equations, Example 11: a ≥ 100, 10 ≤ b < 100, b is an integer
12. Solving Equations, Example 12: a ≥ 100, 10 ≤ b < 100, b is a decimal

1. Solving Equations, Example 13: 0 < a < 10, 0 < b < 10, b is an integer
2. Solving Equations, Example 14: 0 < a < 10, 0 < b < 10, b is a decimal
3. Solving Equations, Example 15: 0 < a < 10, 10 ≤ b < 100, b is an integer
4. Solving Equations, Example 16: 0 < a < 10, 10 ≤ b < 100, b is an integer
5. Solving Equations, Example 17: 0 < a < 10, b ≥ 100, b is an integer
6. Solving Equations, Example 18: 0 < a < 10, b ≥ 100, b is a decimal
7. Solving Equations, Example 19: 10 ≤ a < 100, 0 < b < 10, b is an integer
8. Solving Equations, Example 20: 10 ≤ a < 100, 0 < b < 10, b is a decimal
9. Solving Equations, Example 21: 10 ≤ a < 100, 10 ≤ b < 100, b is an integer
10. Solving Equations, Example 22: 10 ≤ a < 100, 10 ≤ b < 100, b is a decimal
11. Solving Equations, Example 23: 10 ≤ a < 100, b ≥ 100, b is an integer
12. Solving Equations, Example 24: 10 ≤ a < 100, b ≥ 100, b is a decimal
13. Solving Equations, Example 25: a ≥ 100, 0 < b < 10, b is an integer
14. Solving Equations, Example 26: a ≥ 100, 0 < b < 10, b is a decimal
15. Solving Equations, Example 27: a ≥ 100, 10 ≤ b < 100, b is an integer
16. Solving Equations, Example 28: a ≥ 100, 10 ≤ b < 100, b is a decimal
17. Solving Equations, Example 29: a ≥ 100, b ≥ 100, b is an integer
18. Solving Equations, Example 30: a ≥ 100, b ≥ 100, b is a decimal

1. Solving Equations, Example 31: 0 < a < 10, 0 < b < 1
2. Solving Equations, Example 32: 0 < a < 10, 1 ≤ b ≤ 10
3. Solving Equations, Example 33: 0 < a < 10, 10 ≤ b ≤ 99
4. Solving Equations, Example 34: 0 < a < 10, b ≥ 100
5. Solving Equations, Example 35: 10 ≤ a ≤ 100, 0 < b < 1
6. Solving Equations, Example 36: 10 ≤ a ≤ 100, 1 < b ≤ 10
7. Solving Equations, Example 37: 10 ≤ a ≤ 100, 10 ≤ b ≤ 99
8. Solving Equations, Example 38: 10 ≤ a ≤ 100, b ≥ 100
9. Solving Equations, Example 39: a ≥ 100, 0 < b < 1
10. Solving Equations, Example 40: a ≥ 100, 1 < b ≤ 10
11. Solving Equations, Example 41: a ≥ 100, 10 ≤ b ≤ 99
12. Solving Equations, Example 42: a ≥ 100, b ≥ 100

Need more math help? See our Math Solvers, which include math tools for algebra.

Math Tutorials: Slope Formula

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In these examples, find the slope of a line between two points under the conditions shown below. To start, watch the following video, which explains the concept of the slope formula.

1. Slope Formula, Example 1: Both points in Quadrant 1, positive slope.
2. Slope Formula, Example 2: Both points in Quadrant 1, negative slope.
3. Slope Formula, Example 3: Both points in Quadrant 1, zero slope.
4. Slope Formula, Example 4: Both points in Quadrant 1, undefined slope.
5. Slope Formula, Example 5: A point in Q1 and a point in Q2, positive slope.
6. Slope Formula, Example 6: A point in Q1 and a point in Q2, negative slope.
7. Slope Formula, Example 7: A point in Q1 and a point in Q2, zero slope.
8. Slope Formula, Example 8: A point in Q1 and a point in Q3, negative slope.
9. Slope Formula, Example 9: A point in Q1 and a point in Q4, positive slope.
10. Slope Formula, Example 10: A point in Q1 and a point in Q4, negative slope.
11. Slope Formula, Example 11: A point in Q1 and a point in Q4, no slope.
12. Slope Formula, Example 12: A point in Q2 and a point in Q3, positive slope.
13. Slope Formula, Example 13: A point in Q2 and a point in Q3, negative slope.
14. Slope Formula, Example 14: A point in Q2 and a point in Q3, no slope.
15. Slope Formula, Example 15: A point in Q3 and a point in Q4, positive slope.
16. Slope Formula, Example 16: A point in Q3 and a point in Q4, negative slope.
17. Slope Formula, Example 17: A point in Q3 and a point in Q4, zero slope.
18. Slope Formula, Example 18: A point point on the x-axis and point on the y-axis, positive slope.
19. Slope Formula, Example 19: A point point on the x-axis and point on the y-axis, negative slope.
20. Slope Formula, Example 20: A point point on the x-axis and point on the y-axis, zero slope.
21. Slope Formula, Example 21: A point point on the x-axis and point on the y-axis, no slope.

Need more math help? See our Math Solvers, which include math tools for algebra.

Math Tutorials: Graphs of Linear Functions Given the Slope and y-Intercept

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In these examples, construct a graph of a line given the slope and y-intercept, under the following conditions:

1. Example 1: Positive whole number slope, positive y-intercept.
2. Example 2: Positive fractional slope, positive y-intercep.
3. Example 3: Positive whole number slope, negative y-intercept.
4. Example 4: Positive fractional slope, negative y-intercept .
5. Example 5: Negative whole number slope, positive y-intercept .
6. Example 6: Negative fractional slope, positive y-intercept .
7. Example 7: Negative whole number slope, negative y-intercept .
8. Example 8: Negative fractional slope, negative y-intercept .
9. Example 9: Positive slope, y-intercept at the origin.
10. Example 10: Negative slope, y-intercept at the origin .
11. Example 11: Zero slope, positive y-intercept .
12. Example 12: Zero slope, negative y-intercept .
13. Example 13: Zero slope. y-intercept at the origin.

Math Tutorials: Graphs of Absolute Value Functions

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In these examples, graphs of absolute value functions are shown, under the following conditions:

1. Example 1: y = |x|
2. Example 2: y = |cx|, c > 0
3. Example 3: y = |cx|, c < 0
4. Example 4: y = c|x|, c > 0
5. Example 5: y = c|x|, c < 0
6. Example 6: y = |x + c|
7. Example 7: y = |x - c|
8. Example 8: y = |x| + c
9. Example 9: y = |x| - c
10. Example 10: y = |cx + d|
11. Example 11: y = |cx - d|
12. Example 12: y = |-cx + d|
13. Example 13: y = |-cx - d|
14. Example 14: y = |cx + d| + e
15. Example 15: y = |cx - d| + e
16. Example 16: y = |cx+d| - e
17. Example 17: y = |cx - d| - e
18. Example 18: y = |-cx + d| + e
19. Example 19: y = |-cx - d| = e
20. Example 20: y = |-cx + d| - e
21. Example 21: y = |-cx - d| - e

Need more math help? See our Math Solvers, which include math tools for algebra.

Math Tutorials: Graphs of Linear Inequalities

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In these examples, graph a linear inequality under the following conditions:

1. Example 1: y > mx + b, positive slope
2. Example 2: y > mx + b, negative slope
3. Example 3: y > mx + b, zero slope
4. Example 4: y < mx + b, positive slope
5. Example 5: y < mx + b, negative slope
6. Example 6: y < mx + b, zero slope
7. Example 7: y ≥ mx + b, positive slope
8. Example 8: y ≥ mx + b, negative slope
9. Example 9: y ≥ mx + b, zero slope
10. Example 10: y ≤ mx + b, positive slope
11. Example 11: y ≤ mx + b, negative slope
12. Example 12: y ≤ mx + b, zero slope

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Math Tutorials: Midpoint Formula

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In these examples, find the coordinates of the midpoint for any two points, under the following conditions:

1. Example 1: Two points in Quadrant 1, midpoint made up of whole number coordinates.
2. Example 2: Two points in Quadrant 1, midpoint made up of decimal value coordinates.
3. Example 3: One point in Q1, one in Q2, midpoint made up of whole number coordinates.
4. Example 4: One point in Q1, one in Q2, midpoint made up of decimal value coordinates.
5. Example 5: One point in Q2, one in Q3, midpoint made up of whole number coordinates.
6. Example 6: One point in Q2, one in Q3, midpoint made up of decimal value coordinates.
7. Example 7: One point in Q3, one in Q4, midpoint made up of whole number coordinates.
8. Example 8: One point in Q3, one in Q4, midpoint made up of decimal value coordinates.
9. Example 9: One point in Q4, one in Q1, midpoint made up of whole number coordinates.
10. Example 10: One point in Q4, one in Q1, midpoint made up of decimal value coordinates.
11. Example 11: One point in Q1, one on the y-axis, midpoint made up of whole number coordinates.
12. Example 12: One point in Q1, one on the y-axis, midpoint made up of decimal value coordinates.
13. Example 13: One point in Q2, one on the y-axis, midpoint made up of whole number coordinates.
14. Example 14: One point in Q2, one on the y-axis, midpoint made up of decimal value coordinates.
15. Example 15: One point in Q3, one on the y-axis, midpoint made up of whole number coordinates.
16. Example 16: One point in Q3, one on the y-axis, midpoint made up of decimal value coordinates.
17. Example 17: One point in Q4, one on the y-axis, midpoint made up of whole number coordinates.
18. Example 18: One point in Q4, one on the y-axis, midpoint made up of decimal value coordinates.
19. Example 19: One point x-axis, one on the y-axis, midpoint made up of whole number coordinates.
20. Example 20: One point x-axis, one on the y-axis, midpoint made up of decimal value coordinates.

Need more math help? See our Math Solvers, which include math tools for algebra.

Math Tutorials: Distance Formula

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In these examples, find the distance between two points under the following conditions:

1. Example 1: Both points in Quadrant 1, whole number distance.
2. Example 2: Both points in Quadrant 1, distance as an irrational number.
3. Example 3: Both points in Quadrant 1, along a horizontal line.
4. Example 4: Both points in Quadrant 1, along a vertical line.
5. Example 5: A point in Q1 and a point in Q2, whole number distance.
6. Example 6: A point in Q1 and a point in Q2, distance as an irrational number.
7. Example 7: A point in Q1 and a point in Q2, distance along a horizontal line.
8. Example 8: A point in Q1 and a point in Q3, whole number distance.
9. A point in Q1 and a point in Q4, rational number distance.
10. Example 10: A point in Q1 and a point in Q4, distance as an irrational number.
11. A point in Q1 and a point in Q4, along a vertical line.
12. Example 12: A point in Q2 and a point in Q3, whole number distance.
13. Example 13: A point in Q2 and a point in Q3, distance as an irrational number.
14. Example 14: A point in Q2 and a point in Q3, along a vertical line.
15. Example 15: A point in Q3 and a point in Q4, whole number distance.
16. Example 16: A point in Q3 and a point in Q4, distance as an irrational number.
17. Example 17: A point in Q3 and a point in Q4, along a horizontal line.
18. Example 18: A point point on the x-axis and point on the y-axis, whole number distance.
19. A point point on the x-axis and point on the y-axis, distance as an irrational number.
20. Example 20: A point point on the x-axis and point on the y-axis, along a horizontal line.
21. Example 21: A point point on the x-axis and point on the y-axis, along a vertical line.

Need more math help? See our Math Solvers, which include math tools for algebra.

Math Tutorials: Point-Slope Form

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In these examples, find the equation of the line given the slope and a point and the following conditions:

1. Example 1: Positive slope, point in Quadrant 1
2. Example 2: Negative slope, point in Quadrant 1
3. Example 3: Positive slope, point in Quadrant 2
4. Example 4: Negative slope, point in Quadrant 2
5. Example 5: Positive slope, point in Quadrant 3
6. Example 6: Negative slope, point in Quadrant 3
7. Example 7: Positive slope, point in Quadrant 4
8. Example 8: Negative slope, point in Quadrant 4

Need more math help? See our Math Solvers, which include math tools for algebra.

Math Tutorials: Equation of a Line Given Two Points

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In these examples, find the equation of the line given the coordinates of two points on the line and the following conditions:

1. Example 1: Both points in Quadrant 1, positive slope
2. Example 2: Both points in Quadrant 1, negative slope
3. Example 3: Both points in Quadrant 1, zero slope
4. Example 4: Both points in Quadrant 1, no slope
5. Example 5: Both points in Quadrant 2, positive slope
6. Example 6: Both points in Quadrant 2, negative slope
7. Example 7: Both points in Quadrant 2, zero slope
8. Example 8: Both points in Quadrant 2, no slope
9. Example 9: Both points in Quadrant 3, positive slope
10. Example 10: Both points in Quadrant 3, negative slope
11. Example 11: Both points in Quadrant 3, zero slope
12. Example 12: Both points in Quadrant 3, no slope
13. Example 13: Both points in Quadrant 4, positive slope
14. Example 14: Both points in Quadrant 4, negative slope
15. Example 15: Both points in Quadrant 4, zero slope
16. Example 16: Both points in Quadrant 4, no slope
17. Example 17: One point in Q1, one point in Q2, positive slope
18. Example 18: One point in Q1, one point in Q2, negative slope
19. Example 19: One point in Q1, one point in Q2, zero slope
20. Example 20: One point in Q1, one point in Q3, positive slope
21. Example 21: One point in Q1, one point in Q4, positive slope
22. Example 22: One point in Q1, one point in Q4, negative slope
23. Example 23: One point in Q1, one point in Q3, no slope
24. Example 24: One point in Q2, one point in Q3, positive slope
25. Example 25: One point in Q2, one point in Q3, negative slope
26. Example 26: One point in Q2, one point in Q3, no slope
27. Example 27: One point in Q3, one point in Q4, positive slope
28. Example 28: One point in Q3, one point in Q4, negative slope
29. Example 29: One point in Q3, one point in Q4, zero slope

Need more math help? See our Math Solvers, which include math tools for algebra.

Math Tutorials: Graphing Parallel and Perpendicular Lines

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In these examples, graph parallel or perpendicular lines through a given point, under the following conditions:

1. Example 1: Point in Q1 parallel to line with positive slope
2. Example 2: Point in Q1 perpendicular to line with positive slope
3. Example 3: Point in Q1 parallel to line with negative slope
4. Example 4: Point in Q1 perpendicular to line with negative slope
5. Example 5: Point in Q2 parallel to line with positive slope
6. Example 6: Point in Q2 perpendicular to line with positive slope
7. Example 7: Point in Q2 parallel to line with negative slope
8. Example 8: Point in Q2 perpendicular to line with negative slope
9. Example 9: Point in Q3 parallel to line with positive slope
10. Example 10: Point in Q3 perpendicular to line with positive slope
11. Example 11: Point in Q3 parallel to line with negative slope
12. Example 12: Point in Q3 perpendicular to line with negative slope
13. Example 13: Point in Q4 parallel to line with positive slope
14. Example 14: Point in Q4 perpendicular to line with positive slope
15. Example 15: Point in Q4 parallel to line with negative slope
16. Example 16: Point in Q4 perpendicular to line with negative slope
17. Example 17: Point on the positive x-axis parallel to line with positive slope
18. Example 18: Point on the positive x-axis perpendicular to line with positive slope
19. Example 19: Point on the positive x-axis parallel to line with negative slope
20. Example 20: Point on the positive x-axis perpendicular to line with negative slope
21. Example 21: Point on the negative x-axis parallel to line with positive slope
22. Example 22: Point on the negative x-axis perpendicular to line with positive slope
23. Example 23: Point on the negative x-axis parallel to line with negative slope
24. Example 24: Point on the negative x-axis perpendicular to line with negative slope
25. Example 25: Point on the positive y-axis parallel to line with positive slope
26. Example 26: Point on the positive y-axis perpendicular to line with positive slope
27. Example 27: Point on the positive y-axis parallel to line with negative slope
28. Example 28: Point on the positive y-axis perpendicular to line with negative slope
29. Example 29: Point on the negative y-axis parallel to line with positive slope
30. Example 30: Point on the negative y-axis perpendicular to line with positive slope
31. Example 31: Point on the negative y-axis parallel to line with negative slope
32. Example 32: Point on the negative y-axis perpendicular to line with negative slope

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Math Tutorials: Solving Quadratic Equations Graphically

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In these examples, solve a quadratic equation graphically under the following conditions:

1. Solving Equations, Example 1: Two solutions, one positive, one negative. Parabola opens downward.
2. Solving Equations, Example 2: Two solutions, one positive, one negative. Parabola opens upward.
3. Solving Equations, Example 3: Two solutions, both positive. Parabola opens downward.
4. Solving Equations, Example 4: Two solutions, both negative. Parabola opens upward.
5. Solving Equations, Example 5: One solution. Parabola opens downward.
6. Solving Equations, Example 6: One solution. Parabola opens upward.
7. Solving Equations, Example 7: No solutions. Parabola opens upward.
8. Solving Equations, Example 8: No solution. Parabola opens downward.

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Math Tutorials: Completing the Square

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In these examples, solve a quadratic equation using the technique of completing the square, under the following conditions:

1. Example 1: Two solutions, one positive, one negative. Parabola opens downward.
2. Example 2: Two solutions, one positive, one negative. Parabola opens upward.
3. Example 3: Two solutions, both positive. Parabola opens downward.
4. Example 4: Two solutions, both negative. Parabola opens upward.

Completing the Square (an Alternative to the Quadratic Formula)

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Math Tutorials: Quadratic Formula

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Solve a quadratic equation using the quadratic formula under conditions shown below. To start, watch the following video, which explains the concept of the quadratic formula.

1. Solving Equations with the Quadratic Formula, Example 1: Positive values for a, b, and c, two real roots.
2. Solving Equations with the Quadratic Formula, Example 2: Positive values for a, b, and c, one root.
3. Solving Equations with the Quadratic Formula, Example 3: Positive values for a, b, and c, complex roots.
4. Solving Equations with the Quadratic Formula, Example 4: Negative values for a, b, and c, two real root.
5. Solving Equations with the Quadratic Formula, Example 5: Negative values for a, b, and c, one root.
6. Solving Equations with the Quadratic Formula, Example 6: Negative values for a, b, and c, complex root.
7. Solving Equations with the Quadratic Formula, Example 7: Negative value for a, positive for b and c, two real roots.
8. Solving Equations with the Quadratic Formula, Example 8: Negative values for a and c, positive for b, one root.
9. Solving Equations with the Quadratic Formula, Example 9: Negative values for a and c, positive for b, two complex roots.
10. Solving Equations with the Quadratic Formula, Example 10: Positive value for a, negative for b and c, two real roots.
11. Solving Equations with the Quadratic Formula, Example 11: Positive values for a and c, negative for b, one root.
12. Solving Equations with the Quadratic Formula, Example 12: Positive value for a, negative for b and c, two complex roots.

The Quadratic Formula

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Math Tutorials: Factoring Quadratics

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In these examples, quadratic expressions factor into the following product of factors:

1. Example 1: (x + a)(x + b)
2. Example 2: (x - a)(x + b)
3. Example 3: (x + a)(x - b)
4. Example 4: (x - a)(x - b)
5. Example 5: (ax + b)(x + c)
6. Example 6: (ax - b)(x + c)
7. Example 7: (ax + b)(x - c)
8. Example 8: (ax - b)(x - c)
9. Example 9: (x + a)²
10. Example 10: (x - a)²
11. Example 11: (x + a)(x – a)

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Math Tutorials: Polynomial Expansion

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In these examples, the product of three expressions yields a cubic polynomial, under the following conditions:

1. Example 1: x(x + a)(x + b)
2. Example 2: x(x - a)(x + b)
3. Example 3: x(x + a)(x - b)
4. Example 4: x(x - a)(x - b)
5. Example 5: (x + a)(x + b)(x + c)
6. Example 6: (x - a)(x + b)(x + c)
7. Example 7: (x + a)(x - b)(x + c)
8. Example 8: (x + a)(x + b)(x - c)
9. Example 9: (x - a)(x - b)(x + c)
10. Example 10: (x - a)(x + b)(x - c)
11. Example 11: (x + a)(x - b)(x - c)
12. Example 12: (x - a)(x - b)(x - c)

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Math Tutorials: FOIL Method

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1. 1. Example of the form (x + a)(x + b).
2. 2. Example of the form (x - a)(x + b).
3. 3. Example of the form (x + a)(x - b).
4. 4. Example of the form (x - a)(x - b).
5. 5. Example of the form (ax + b)(x + c).
6. 6. Example of the form (ax - b)(x + c).
7. 7. Example of the form (ax + b)(x - c).
8. 8. Example of the form (ax - b)(x - c).
9. 9. Example of the form (ax + b)(cx + d).
10. 10. Example of the form (ax - b)(cx + d).
11. 11. Example of the form (ax + b)(cx - d).
12. 12. Example of the form (ax - b)(cx - d).
13. 13. Example of the form (-ax + b)(cx + d).
14. 14. Example of the form (-ax - b)(cx + d).
15. 15. Example of the form (-ax + b)(cx - d).
16. 16. Example of the form (-ax - b)(cx - d).
17. 17. Example of the form (-ax - b)(-cx - d).

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Math Tutorials: Laws of Exponents

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Simplifying exponential expressions of the form under the following conditions:

1. Example 1: a > 0, b > 0.
2. Example 2: a < 0, b > 0.
3. Example 3: a > 0, b < 0.
4. Example 4: a < 0, b < 0.

Simplifying exponential expressions of the form under the following conditions:

1. Example 5: a > 0, b > 0, c > 0.
2. Example 6: a < 0, b > 0, c > 0.
3. Example 7: a > 0, b < 0, c > 0.
4. Example 8: a > 0, b > 0, c < 0.
5. Example 9: a < 0, b < 0, c > 0.
6. Example 10: a > 0, b < 0, c < 0.
7. Example 11: a < 0, b > 0, c < 0.
8. Example 12: a < 0, b < 0, c < 0.

Simplifying exponential expressions of the form under the following conditions:

1. Example 13: a > 0, b > 0.
2. Example 14: a < 0, b > 0.
3. Example 15: a > 0, b < 0.
4. Example 16: a < 0, b < 0.

Simplifying exponential expressions of the form under the following conditions:

1. Example 17: a > 0, b > 0, c > 0.
2. Example 18: a < 0, b > 0, c > 0.
3. Example 19: a > 0, b < 0, c > 0.
4. Example 20: a > 0, b > 0, c < 0.
5. Example 21: a < 0, b < 0, c > 0.
6. Example 22: a > 0, b < 0, c < 0.
7. Example 23: a < 0, b > 0, c < 0.
8. Example 24: a < 0, b < 0, c < 0.

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Math Tutorials: Exponential Functions

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Examples of graphs of exponential functions of the form
y = a * b^(cx), under the following conditions:

1. Example 1: 0 < b < 1, a = 1, c = 1.
2. Example 2: 0 < b < 1, a = 1, c > 1.
3. Example 3: 0 < b < 1, a = 1, c < 0.
4. Example 4: 0 < b < 1, a = 1, 0< c < 1.
5. Example 5: 0 < b < 1, a > 0, c = 1.
6. Example 6: 0 < b < 1, a < 0, c = 1.
7. Example 7: 0 < b < 1, a > 0, c > 1.
8. Example 8: 0 < b < 1, a < 0, c > 1.
9. Example 9: 0 < b < 1, a > 0, 0 < c < 1.
10. Example 10: 0 < b < 1, 0 < c < 1.
11. Example 11: b = 2, a = 1, c = 1.
12. Example 12: b = 2, a = 1, c > 1.
13. Example 13: b = 2, a = 1, c < 0.
14. Example 14: b = 2, a = 1, 0< c < 1.
15. Example 15: b = 2, a > 0, c = 1.
16. Example 16: b = 2, a < 0, c = 1.
17. Example 17: b = 2, a > 0, c > 1.
18. Example 18: b = 2, a < 1, c > 1.
19. Example 19: b = 2, a > 0, 0 < c < 1.
20. Example 20: b = 2, a < 0, 0 < c < 1.
21. Example 21: b = e, a = 1, c = 1.
22. Example 22: b = e, a = 1, c > 1.
23. Example 23: b = e, a = 1, c < 0.
24. Example 24: b = e, a = 1, 0< c < 1.
25. Example 25: b = e, a > 0, c = 1.
26. Example 26: b = e, a < 0, c = 1.
27. Example 27: b = e, a > 0, c > 1.
28. Example 28: b = e, a < 1, c > 1.
29. Example 29: b = e, a > 0, 0 < c < 1.
30. Example 30: b = e, a < 0, 0 < c < 1.
31. Example 31: b = 10, a = 1, c = 1.
32. Example 32: b = 10, a = 1, c > 1.
33. Example 33: b = 10, a = 1, c < 0.
34. Example 34: b = 10, a = 1, 0< c < 1.
35. Example 35: b = 10, a > 0, c = 1.
36. Example 36: b = 10, a < 0, c = 1.
37. Example 37: b = 10, a > 0, c > 1.
38. Example 38: b = 10, a < 1, c > 1.
39. Example 39: b = 10, a > 0, 0 < c < 1.
40. Example 40: b = 10, a < 0, 0 < c < 1.

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Math Tutorials: Logarithmic Functions

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Examples of graphs of logarithmic functions, under the following conditions:

1. Example 1: log(x).
2. Example 2: -log(x).
3. Example 3: log(cx).
4. Example 4: -log(cx).
5. Example 5: log(cx + d).
6. Example 6: log(cx - d).
7. Example 7: log(cx) + d.
8. Example 8: log(cx) - d.
9. Example 9: -log(cx) + d.
10. Example 10: -log(cx) - d.
11. Example 11: log(cx + d) + e.
12. Example 12: log(cx - d) + e.
13. Example 13: log(cx + d) - e.
14. Example 14: log(cx + d) - e.
15. Example 15: ln(x).
16. Example 16: -ln(x).
17. Example 17: ln(cx).
18. Example 18: -ln(cx).
19. Example 19: ln(cx + d).
20. Example 20: ln(cx - d).
21. Example 21: ln(cx) + d.
22. Example 22: ln(cx) - d.
23. Example 23: -ln(cx) + d.
24. Example 24: -ln(cx) - d.
25. Example 25: ln(cx + d) + e.
26. Example 26: ln(cx - d) + e.
27. Example 27: ln(cx + d) - e.
28. Example 28: ln(cx + d) - e.

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Math Tutorials: Rational Functions

SLIDE SHOW PREVIEW

Examples of graphs of rational functions, under the following conditions:

1. Algebra Tutorial 1: y = 1/x.
2. Algebra Tutorial 2: y = -1/x.
3. Algebra Tutorial 3: y = 1/(x + c).
4. Algebra Tutorial 4: y = 1/(x - c).
5. Algebra Tutorial 5: y = 1/(cx + d).
6. Algebra Tutorial 6: y = -1/(cx + d).
7. Algebra Tutorial 7: y = 1/(cx - d).
8. Algebra Tutorial 8: y = 1/(-cx + d).
9. Algebra Tutorial 9: y = (x + a)/(x + b).
10. Algebra Tutorial 10: y = (x - a)/(x + b).
11. Algebra Tutorial 11: y = (x - a)/(x - b).
12. Algebra Tutorial 12: y = (x + a)/[(x + b)(x + c)].
13. Algebra Tutorial 13: y = (x - a)/[(x + b)(x + c)].
14. Algebra Tutorial 14: y = (x + a)/[(x - b)(x + c)].
15. Algebra Tutorial 15: y = (x + a)/[(x + b)(x - c)].
16. Algebra Tutorial 16: y = (x - a)/[(x - b)(x + c)].
17. Algebra Tutorial 17: y = (x - a)/[(x + b)(x - c)].
18. Algebra Tutorial 18: y = (x - a)/[(x - b)(x - c)].
19. Algebra Tutorial 19: y = -(x + a)/(x + b).
20. Algebra Tutorial 20: y = -(x - a)/(x + b).
21. Algebra Tutorial 21: y = -(x - a)/(x - b).
22. Algebra Tutorial 22: y = -(x + a)/[(x + b)(x + c)].
23. Algebra Tutorial 23: y = -(x - a)/[(x + b)(x + c)].
24. Algebra Tutorial 24: y = -(x + a)/[(x - b)(x + c)].
25. Algebra Tutorial 25: y = -(x + a)/[(x + b)(x - c)].
26. Algebra Tutorial 26: y = -(x - a)/[(x - b)(x + c)].
27. Algebra Tutorial 27: y = -(x - a)/[(x + b)(x - c)].
28. Algebra Tutorial 28: y = (x - a)/[(x - b)(x - c)].

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Math Tutorials: Rational Expressions

SLIDE SHOW PREVIEW

Examples of combining rational expressions, under the following conditions:

1. Math Tutorial 1
2. Math Tutorial 2
   


3. Math Tutorial 3
4. Math Tutorial 4
5. Math Tutorial 5
6. Math Tutorial 6
7. Math Tutorial 7
8. Math Tutorial 8


9. Math Tutorial 9
10. Math Tutorial 10
11. Math Tutorial 11
12. Math Tutorial 12


13. Math Tutorial 13
14. Math Tutorial 14
15. Math Tutorial 15
16. Math Tutorial 16
17. Math Tutorial 17


18. Math Tutorial 18
19. Math Tutorial 19
20. Math Tutorial 20
21. Math Tutorial 21
22. Math Tutorial 22
23. Math Tutorial 23
24. Math Tutorial 24


25. Math Tutorial 25
26. Math Tutorial 26
27. Math Tutorial 27
28. Math Tutorial 28

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Math Tutorials: Conic Sections

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Graphing a conic section of the form (x – h)² + (y – k)² = r², under the following conditions:

1. Algebra Tutorial 1: Centered at the origin
2. Algebra Tutorial 2: Centered on the x-axis
3. Algebra Tutorial 3: Centered on the y-axis
4. Algebra Tutorial 4: Centered in quadrant 1
5. Algebra Tutorial 5: Centered in quadrant 2
6. Algebra Tutorial 6: Centered in quadrant 3
7. Algebra Tutorial 7: Centered in quadrant 4

Graphing a conic section of the form (y – k)² – (x – h) = 0, under the following conditions:

1. Algebra Tutorial 8: Vertex at the origin
2. Algebra Tutorial 9: Vertex on the x-axis
3. Algebra Tutorial 10: Vertex on the y-axis
4. Algebra Tutorial 11: Vertex in quadrant 1
5. Algebra Tutorial 12: Vertex in quadrant 2
6. Algebra Tutorial 13: Vertex in quadrant 3
7. Algebra Tutorial 14: Vertex in quadrant 4

Graphing a conic section of the form (x – k)² – (y – h) = 0, under the following conditions:

1. Algebra Tutorial 15: Vertex at the origin
2. Algebra Tutorial 16: Vertex on the x-axis
3. Algebra Tutorial 17: Vertex on the y-axis
4. Algebra Tutorial 18: Vertex in quadrant 1
5. Algebra Tutorial 19: Vertex in quadrant 2
6. Algebra Tutorial 20: Vertex in quadrant 3
7. Algebra Tutorial 21: Vertex in quadrant 4

Graphing a conic section of the form
(x – h)²/a² + (y – k)²/b² = 1, under the following conditions:

1. Algebra Tutorial 22: Centered at the origin, a > b
2. Algebra Tutorial 23: Centered at the origin, b > a
3. Algebra Tutorial 24: Centered on the x-axis, a > b
4. Algebra Tutorial 25: Centered on the x-axis, b > a
5. Algebra Tutorial 26: Centered on the y-axis, a > b
6. Algebra Tutorial 27: Centered on the y-axis, b > a
7. Algebra Tutorial 28: Centered in quadrant 1, a > b
8. Algebra Tutorial 29: Centered in quadrant 1, b > a
9. Algebra Tutorial 30: Centered in quadrant 2, a > b
10. Algebra Tutorial 31: Centered in quadrant 2, b > a
11. Algebra Tutorial 32: Centered in quadrant 3, a > b
12. Algebra Tutorial 33: Centered in quadrant 3, b > a
13. Algebra Tutorial 34: Centered in quadrant 4, a > b
14. Algebra Tutorial 35: Centered in quadrant 4, b > a

Graphing a conic section of the form
(x – h)²/a² - (y – k)²/b² = 1, or
-(x – h)²/a² + (y – k)²/b² = 1, under the following conditions:

1. Algebra Tutorial 36: Centered at the origin, horizontal major axis
2. Algebra Tutorial 37: Centered at the origin, vertical major axis
3. Algebra Tutorial 38: Centered on the x-axis, horizontal major axis
4. Algebra Tutorial 39: Centered on the x-axis, vertical major axis
5. Algebra Tutorial 40: Centered on the y-axis, horizontal major axis
6. Algebra Tutorial 41: Centered on the y-axis, vertical major axis
7. Algebra Tutorial 42: Centered in quadrant 1, horizontal major axis
8. Algebra Tutorial 43: Centered in quadrant 1, vertical major axis
9. Algebra Tutorial 44: Centered in quadrant 2, horizontal major axis
10. Algebra Tutorial 45: Centered in quadrant 2, vertical major axis
11. Algebra Tutorial 46: Centered in quadrant 3, horizontal major axis
12. Algebra Tutorial 47: Centered in quadrant 3, vertical major axis
13. Algebra Tutorial 48: Centered in quadrant 4, horizontal major axis
14. Algebra Tutorial 49: Centered in quadrant 4, vertical major axis

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