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Write the equation of the parabola in vertex form with the following condition Focus: (2,2) Directrix: x = -2. O (y-2)² = 8x ○ (y-2)² = 8(x − 2) (y + 2)²2 = 8x O(y-2)² = -8x

Write the equation of the parabola in vertex form with the following condition Focus: (2,2) Directrix: x = -2. O (y-2)² = 8x ○ (y-2)² = 8(x − 2) (y + 2)²2 = 8x O(y-2)² = -8x

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Parabola Equation in Vertex Form In this exercise, you are required to write the equation of a parabola in vertex form given the following conditions: - **Focus:** (2,2) - **Directrix:** x = -2 #### Multiple Choice Options: You need to choose the correct equation from the options given below: 1. (y - 2)² = 8x 2. (y - 2)² = 8(x - 2) 3. (y + 2)² = 8x 4. (y - 2)² = -8x #### Explanation: To determine the correct equation, you should use the formula for the equation of a parabola in vertex form, which is typically given as \((y - k)^2 = 4p(x - h)\) where \((h, k)\) represents the vertex. Given the focus and directrix, you can determine the value of \(p\), the distance from the vertex to the focus or directrix. Use this information to transform the equation into the correct format. ### Graphs and Diagrams: In this case, there are no graphs or diagrams provided within the given content. The image simply lists the multiple-choice options after stating the conditions for the parabola's equation. ### Instructions for Use on Educational Website: 1. **Statement of the Problem:** Clearly describe the problem statement as given above. 2. **Answer Choices:** List the multiple-choice options provided. 3. **Explanation Section:** Include a detailed explanation on how to derive the correct equation using the given focus and directrix. 4. **Interactive Component:** Optionally, add an interactive component where students can solve for the vertex and the value of \(p\) based on given conditions. This content aims to help students understand how to form the equation of a parabola in vertex form using given geometric conditions.
Transcribed Image Text:### Parabola Equation in Vertex Form In this exercise, you are required to write the equation of a parabola in vertex form given the following conditions: - **Focus:** (2,2) - **Directrix:** x = -2 #### Multiple Choice Options: You need to choose the correct equation from the options given below: 1. (y - 2)² = 8x 2. (y - 2)² = 8(x - 2) 3. (y + 2)² = 8x 4. (y - 2)² = -8x #### Explanation: To determine the correct equation, you should use the formula for the equation of a parabola in vertex form, which is typically given as \((y - k)^2 = 4p(x - h)\) where \((h, k)\) represents the vertex. Given the focus and directrix, you can determine the value of \(p\), the distance from the vertex to the focus or directrix. Use this information to transform the equation into the correct format. ### Graphs and Diagrams: In this case, there are no graphs or diagrams provided within the given content. The image simply lists the multiple-choice options after stating the conditions for the parabola's equation. ### Instructions for Use on Educational Website: 1. **Statement of the Problem:** Clearly describe the problem statement as given above. 2. **Answer Choices:** List the multiple-choice options provided. 3. **Explanation Section:** Include a detailed explanation on how to derive the correct equation using the given focus and directrix. 4. **Interactive Component:** Optionally, add an interactive component where students can solve for the vertex and the value of \(p\) based on given conditions. This content aims to help students understand how to form the equation of a parabola in vertex form using given geometric conditions.
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