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Write an equation of the parabola shown. Ay -4 2 vertex focus -2 2 4 6 8 x -2 (1.5, 0) -4 An equation of the parabola is

Write an equation of the parabola shown. Ay -4 2 vertex focus -2 2 4 6 8 x -2 (1.5, 0) -4 An equation of the parabola is

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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## Understanding Parabolas: Graph Example ### Objective This example guides you through writing the equation of a given parabola based on its graph. ### Graph Details - **Axes Information**: The graph shows a standard Cartesian coordinate plane with the x-axis and y-axis labeled. The x-axis ranges from -2 to 8, and the y-axis from -4 to 4. - **Parabola Description**: - **Direction**: The parabola opens to the right. - **Vertex**: Marked in green at point (0, 0). This is the starting point of the parabola. - **Focus**: Marked in red at point (1.5, 0) on the x-axis. This point helps define the shape and direction of the parabola. ### Equation of the Parabola The task is to determine the equation of this parabola. Given that the vertex is at (0, 0) and the parabola opens horizontally, its standard form should be: \[ y^2 = 4px \] Where \( p \) is the distance from the vertex to the focus. ### Calculation - **Distance \( p \)**: The focus is at (1.5, 0), so \( p = 1.5 \). - **Equation**: Substituting \( p \) into the standard form: \[ y^2 = 6x \] Thus, the equation of the parabola is: \[ y^2 = 6x \] ### Conclusion This graph and equation demonstrate how the vertex and focus determine the structure and direction of a parabola.
Transcribed Image Text:## Understanding Parabolas: Graph Example ### Objective This example guides you through writing the equation of a given parabola based on its graph. ### Graph Details - **Axes Information**: The graph shows a standard Cartesian coordinate plane with the x-axis and y-axis labeled. The x-axis ranges from -2 to 8, and the y-axis from -4 to 4. - **Parabola Description**: - **Direction**: The parabola opens to the right. - **Vertex**: Marked in green at point (0, 0). This is the starting point of the parabola. - **Focus**: Marked in red at point (1.5, 0) on the x-axis. This point helps define the shape and direction of the parabola. ### Equation of the Parabola The task is to determine the equation of this parabola. Given that the vertex is at (0, 0) and the parabola opens horizontally, its standard form should be: \[ y^2 = 4px \] Where \( p \) is the distance from the vertex to the focus. ### Calculation - **Distance \( p \)**: The focus is at (1.5, 0), so \( p = 1.5 \). - **Equation**: Substituting \( p \) into the standard form: \[ y^2 = 6x \] Thus, the equation of the parabola is: \[ y^2 = 6x \] ### Conclusion This graph and equation demonstrate how the vertex and focus determine the structure and direction of a parabola.
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