Illustrative Math Alignment: Grade 8 Unit 3

Topic

Linear Functions

Description

This example demonstrates the creation of a table of x-y coordinates and the graphing of the linear function y = 5x. The image displays both a graph and a table representing this function. The table includes coordinate pairs (0, 0), (1, 5), (2, 10), (3, 15), and (4, 20), illustrating how the y-value increases by 5 for each unit increase in x.

Topic

Linear Functions

Description

This example showcases the process of creating a table of x-y coordinates and graphing the linear function y = -2x + 5. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 5), (1, 3), (2, 1), (3, -1), and (4, -3), demonstrating how the y-value decreases by 2 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the creation of a table of x-y coordinates and the graphing of the linear function y = -3x - 4. The image displays both a graph and a table representing this function. The table includes coordinate pairs (0, -4), (1, -7), (2, -10), (3, -13), and (4, -16), showing how the y-value decreases by 3 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates how to create a table of x-y coordinates and graph the linear function y = -6x. The image shows both a graph and a table representing this function. The table includes coordinate pairs (0, 0), (1, -6), (2, -12), (3, -18), and (4, -24), illustrating how the y-value decreases by 6 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = x + 7. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 7), (1, 8), (2, 9), (3, 10), and (4, 11), showing how the y-value increases by 1 for each unit increase in x.

Topic

Linear Functions

Description

This example demonstrates the creation of a table of x-y coordinates and the graphing of the linear function y = x - 8. The image displays both a graph and a table representing this function. The table includes coordinate pairs (0, -8), (1, -7), (2, -6), (3, -5), and (4, -4), illustrating how the y-value increases by 1 for each unit increase in x.

Topic

Linear Functions

Description

This example illustrates the process of creating a table of x-y coordinates and graphing the linear function y = x. The image presents both a graph and a table for this function. The table includes coordinate pairs (0, 0), (1, 1), (2, 2), (3, 3), and (4, 4), showing how the y-value increases by 1 for each unit increase in x.

Topic

Quadratics

Description

This example illustrates the relationship between quadratic functions and their graphical representations. The image shows a table of values and the corresponding graph of a quadratic function, highlighting how changes in the equation affect the graph's shape and position. Understanding this relationship is crucial for interpreting and predicting the behavior of quadratic functions. Skills involved include plotting points, recognizing parabolic shapes, and analyzing vertex and axis of symmetry.

Topic

Quadratics

Topic

Quadratics

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. This example highlights the relationship between the equation and its graph, showing the parabolic curve and how it opens downward. Key features such as the vertex and intercepts are easily identifiable, which are crucial for understanding the function's behavior.

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The example illustrates how the coefficients in the quadratic equation affect the graph's shape and direction, allowing for a deeper understanding of the function's properties.

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. This example shows the symmetry of the parabola and how the vertex acts as a turning point, which is critical for graph analysis and interpretation.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The graph clearly shows the parabola's opening direction and the impact of the quadratic term, aiding in the comprehension of graph transformations.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The example demonstrates how the vertex form of the equation can be used to predict the graph's position and shape, enhancing understanding of vertex transformations.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The graphic representation is useful for identifying roots and how they correspond to the x-intercepts of the graph, which is fundamental for solving quadratic equations graphically.

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The graphical representation is useful for determining the kind of discriminant and the number of roots, which is visually represented by the points where the graph intersects the x-axis.

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. These representations are useful to show the axis of symmetry can be used to find the vertex and how this symmetry is reflected in the graph.

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

Topic

Quadratics

Description

This example demonstrates the concept of quadratic functions through a table of values and its graph. It emphasizes how the quadratic function translates into a parabolic graph, showcasing the vertex and symmetry. This visual representation aids in comprehending the impact of coefficients on the graph's curvature and direction. Mastery of this concept involves skills in graphing, interpreting quadratic equations, and identifying key features such as intercepts and vertex.

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. This example shows a downwardly opening parabola and you can see the relationship between the parameters of the function and how they are displayed graphically.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The example shows an upwardly opening parabola. Make a note of the parameters of the function and how they are reflected in the table and graph.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The focus is on understanding how the graph's vertex and axis of symmetry relate to the equation, enhancing skills in graph interpretation.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. It demonstrates the role of the quadratic terms in determining the graph's curvature and the significance of intercepts 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

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The example shows an upwardly opening parabola and you can see the graph's symmetry and how it can be used to predict the function's behavior and solve equations graphically.

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. It highlights the alternative to the quadratic formula in finding roots and how these roots are represented graphically as x-intercepts.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The example shows a function with no roots, since the graph does not intersect the x-axis.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The focus is on understanding how the graph's vertex and axis of symmetry relate to the equation, enhancing skills in graph interpretation.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. It demonstrates the role of the quadratic terms in determining the graph's curvature and the significance of intercepts 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

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. This example demonstrates the relationship between the quadratic equation and its graph, highlighting the vertex and axis of symmetry, which are key to understanding the function's behavior.

Topic

Quadratics

Description

This example illustrates a quadratic function through both a tabular data set and its corresponding graph. The table presents specific input-output pairs that, when plotted, form a parabolic curve on the graph. This visual representation highlights the quadratic function's key features, such as the vertex, axis of symmetry, and intercepts. The table allows for a clear understanding of how each value corresponds to a point on the graph, demonstrating the function's behavior over a range of inputs.

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The example illustrates how changes in coefficients affect the parabola's direction and width, providing insight into graph transformations.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. This example shows a downwardly opening parabola.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The graph and table illustrate the importance of intercepts and how they relate to the roots of the quadratic equation.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. This example shows an upwardly opening parabola that doesn't intersect the x-axis.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. This example shows a downwardly opening parabola that intersects the x-axis at two points.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. The example shows an upwardly opening parabola that intersects the x-axis at two points.

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

Topic

Quadratics

Description

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. It demonstrates the role of the quadratic terms in determining the graph's curvature and the significance of intercepts 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

In this example, a quadratic function is shown in tabular and graphic format. Analyzing these different representations of a function is important and provides relevant information about the quadratic function. This example shows a downwardly opening parabola that has two roots, one of them shown in the table.

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

Topic

Quadratics

Topic

Quadratics

Description

This example provides a quadratic function displayed in both tabular and graphical forms. The table lists values that, when plotted, create a parabolic curve on the graph. This visual representation helps in identifying key features such as the vertex, axis of symmetry, and roots. By analyzing these features, students can understand the impact of different coefficients on the shape and position of the parabola. Skills involved include interpreting data from tables, graphing functions, and understanding the vertex and standard forms of quadratic equations.

Topic

Quadratics

Description

In this example, a quadratic function is presented through both tabular and graphical forms. The accompanying image provides a visual interpretation of the function, emphasizing the relationship between the x-values and their corresponding y-values. This representation allows learners to recognize the nature of quadratic functions, particularly how changes to the function parameters affect the shape and position of the graph. The skills required include critical graph analysis, understanding symmetry in parabolas, and solving for x-intercepts.

Topic

Quadratics

Description

A detailed view of a quadratic function is depicted here, where the data table and graph work in conjunction to showcase the solution process for the function. Analyzing this illustration aids in comprehending how the quadratic function applies to specific scenarios and enhances one’s ability to derive equations from graphs. Such comparative analysis of multiple representations bolsters problem-solving skills and equips students with the tools to tackle different forms of quadratic equations.

Topic

Quadratics

Description

This image presents a quadratic function in tabular and graphic format. The graph reflects the nature of parabolic functions, while the table reinforces the numerical data needed for graphing. By exploring both representations, students can appreciate the convergence of algebra and geometry, honing their capacity for critical thinking and analysis. Understanding the properties of the parabola is essential for mastery in quadratic equations by applying skills such as completing the square or using the quadratic formula.

Topic

Quadratics

Description

This example consolidates the properties of quadratic functions by using a table to present values and a graph to illustrate their relationship. The significance of identifying intercepts, the vertex, and axis of symmetry becomes apparent when viewed together. Mastering these concepts through multiple formats allows for invaluable preparation for advanced algebraic topics, thereby enhancing overall mathematical comprehension and problem-solving abilities.

Topic

Rational Functions

Description

This example demonstrates the graph of the rational function y = 1 / x. The graph is a hyperbola with vertical and horizontal asymptotes, with the vertical asymptote occurring at x = 0. Students are tasked with graphing the function and determining its vertical asymptote.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = (x - 5) / (x + 4). The graph features a vertical asymptote at x = -4 and displays two branches, one in the first quadrant and one in the third quadrant. Students are asked to graph the function and identify its vertical asymptote.

Topic

Rational Functions

Description

This example showcases the graph of the rational function y = (x - 1) / (x - 3). The graph features a vertical asymptote at x = 3 and displays two distinct branches, one in the first quadrant and another in the third quadrant. Students are tasked with graphing the function and identifying its vertical asymptote.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = (x + 1) / ((x + 2)(x + 4)). The graph features two vertical asymptotes at x = -2 and x = -4, and displays three distinct branches, with one in each of the first, second, and third quadrants. Students are asked to graph the function and identify its vertical asymptotes.

Topic

Rational Functions

Description

This example presents the graph of the rational function y = (x - 3) / ((x + 3)(x + 5)). The graph features vertical asymptotes at x = -3 and x = -5, illustrating how the function behaves near these lines. Students are tasked with graphing the function and determining its vertical asymptotes.

Topic

Rational Functions

Description

This example illustrates the graph of the rational function y = (x + 3) / ((x - 1)(x + 4)). The graph features vertical asymptotes at x = -4 and x = 1, displaying how the function behaves near these lines. Students are asked to graph the function and identify its vertical asymptotes.