Illustrative Math Alignment: Grade 6 Unit 7

Topic

Quadratics

Topic

Quadratics

Description

This example demonstrates factoring a quadratic expression where in standard form where a = 1. The process still involves finding two numbers that multiply to give c and add up to b. For example, if the expression is x² - x - 12, we look for factors of -12 that add up to -1, resulting in (x - 4)(x + 3). This skill is essential for solving a wide range of quadratic equations and understanding the relationship between a quadratic's factors and its roots. It also helps in visualizing how the factored form relates to the graph of the parabola, particularly its x-intercepts.

Topic

Quadratics

Topic

Quadratics

Description

In this example, the quadratic function is presented in factored form, highlighting its roots and facilitating the graphing process. Unlike the standard form, the factored form provides immediate insight into the x-intercepts of the graph, allowing for a quick and accurate sketch of the parabola. This form is particularly useful for visualizing the solutions of the equation and understanding the function's behavior.

Topic

Quadratics

Description

This example demonstrates the graphing of a quadratic function in factored form. The factored form is advantageous because it clearly indicates where the graph will intersect the x-axis, making it easier to plot the parabola accurately. This form simplifies the process of identifying the roots and understanding the quadratic's graphical representation.

Topic

Quadratics

Description

The factored form of this quadratic function allows for easy identification of the roots, which are the x-intercepts of the graph. This form is different from the standard form in that it directly provides the points where the parabola crosses the x-axis, simplifying the graphing process. This example illustrates how the factored form can be used to quickly and effectively graph a quadratic function.

Topic

Quadratics

Description

This example highlights the advantages of using the factored form for graphing quadratic functions. The factored form makes it straightforward to determine the roots, which are the x-intercepts of the graph. This simplifies the process of plotting the parabola and understanding the function's behavior, as the roots are immediately visible and can be used to sketch the graph accurately.

Topic

Quadratics

Description

The factored form of a quadratic function provides a clear and efficient way to graph the function by identifying the roots directly. This example shows how the factored form differs from the standard form by offering immediate insight into the x-intercepts, simplifying the graphing process and enhancing understanding of the function's graphical representation.

Topic

Quadratics

Description

In this example, the quadratic function is expressed in factored form, which simplifies the process of graphing by providing the roots directly. This form contrasts with the standard form, where additional calculations are needed to find the roots. The factored form allows for a more straightforward and intuitive graphing process, as it clearly indicates the x-intercepts of the parabola.

Topic

Quadratics

Description

This example illustrates the benefits of using the factored form for graphing quadratic functions. The factored form provides immediate information about the roots, making it easier to sketch the parabola by pinpointing the x-intercepts. This form is a simpler alternative to the standard form when graphing, as it eliminates the need for additional calculations to determine the roots.

Topic

Quadratics

Description

Factoring is a technique used to solve quadratic equations by expressing them as a product of binomials. Once in factored form, finding the roots of the quadratic becomes straightforward as it involves setting each binomial equal to zero. In this example, the quadratic equation is factored into two binomials, allowing for easy identification of the roots. The graphic illustrates the step-by-step process of factoring and solving, highlighting the efficiency of this method for certain types of quadratic equations.

Topic

Quadratics

Description

This example demonstrates solving a quadratic equation by factoring. The equation is rewritten as a product of binomials, simplifying the process of finding the roots. The graphic shows how each binomial is set to zero to find the solutions, illustrating the straightforward nature of this method when applicable.

For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.

Topic

Quadratics

Description

In this example, the quadratic equation is solved by factoring, which involves expressing the equation as a product of binomials. The process makes it easy to find the roots by setting each factor equal to zero. The graphic provides a detailed walkthrough of the factoring steps, showcasing the simplicity and effectiveness of this approach for solving quadratics.

For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.

Topic

Quadratics

Description

This example illustrates the process of solving a quadratic equation by factoring. The equation is factored into binomials, and the roots are found by setting each binomial to zero. The graphic highlights the steps involved in factoring and solving, emphasizing the method's efficiency for certain quadratic equations.

For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.

Topic

Quadratics

Description

In this example, the quadratic equation is solved by factoring, a method that involves rewriting the equation as a product of binomials. This approach simplifies finding the roots, as each binomial is set to zero to solve for the variable. The graphic provides a step-by-step guide to the factoring process, demonstrating its practicality and ease of use.

For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.

Topic

Quadratics

Description

This example demonstrates solving a quadratic equation by factoring. The equation is expressed as a product of binomials, allowing for straightforward determination of the roots by setting each factor to zero. The graphic illustrates the factoring process, highlighting its effectiveness for solving quadratic equations.

For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.

Topic

Quadratics

Description

In this example, the quadratic equation is solved by factoring, which involves expressing it as a product of binomials. This method simplifies finding the roots, as each binomial is set to zero. The graphic provides a clear demonstration of the factoring process, showcasing its simplicity and utility in solving quadratic equations.

For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.

Topic

Quadratics

Description

This example illustrates solving a quadratic equation by factoring. The equation is rewritten as a product of binomials, and the roots are found by setting each factor to zero. The graphic highlights the steps involved in factoring and solving, emphasizing the method's efficiency and applicability to certain quadratic equations.

For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.

This Teacher's Guide provides an overview of the 11 worked-out examples that show how to factor quadratic expressions.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Topic

Multiplication and Division

Description

A Factor is a number that divides another number without leaving a remainder. Examples include factors of 6 (1, 2, 3, 6) and factors of 8 (1, 2, 4, 8). Understanding factors supports number decomposition and multiplication. This term relates to division and multiplication, laying a foundation for understanding divisibility and multiples.

Topic

Multiplication and Division

Topic

Multiplication and Division

This is part of a collection of math quizzes on the topic of Factoring Quadratics.

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Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of Factoring Quadratics.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of Factoring Quadratics.

Related Resources

Quiz Library

ary">click on this link.

In this set of interactive flash cards students practice factoring quadratic polynomials.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

Topic

Polynomials

Description

Factored Polynomial: Expressing a polynomial as the product of two or more lower-degree polynomial terms. Examples: x2 + 3x + 2 = (x + 1)(x + 2), x2 - 7x + 12 = (x - 3)(x - 4), x3 - 1 = (x - 1)(x2 + x + 1). Focuses on a special case of polynomial factoring, emphasizing quadratics.

Topic

Polynomials

Description

Factored Polynomial: Expressing a polynomial as the product of two or more lower-degree polynomial terms. Examples: x2 + 3x + 2 = (x + 1)(x + 2), x2 - 7x + 12 = (x - 3)(x - 4), x3 - 1 = (x - 1)(x2 + x + 1). Focuses on a special case of polynomial factoring, emphasizing quadratics.

Topic

Polynomials

Description

Factored Quadratic: Expressing a polynomial of degree 2 as the product of one or two linear terms. Examples: x2 + 2x + 1 = (x + 1)2, x2 - 7x + 12 = (x - 3)(x - 4), x2 - 2x = x(x - 2). Highlights the use of factorial in binomial expansions and permutations.