RADICALS AND QUADRATIC EQUATIONS 1/5 Finding the x-intercept(s) and the vertex of a parabola Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x²+8x+16. If there is more than one x-intercept, separate them with comma x-intercept(s): 0 0.0 X 5 ? vertex: GD
RADICALS AND QUADRATIC EQUATIONS 1/5 Finding the x-intercept(s) and the vertex of a parabola Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x²+8x+16. If there is more than one x-intercept, separate them with comma x-intercept(s): 0 0.0 X 5 ? vertex: GD
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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![**Finding the x-intercept(s) and the vertex of a parabola**
**Problem Statement:**
Find the x-intercept(s) and the coordinates of the vertex for the parabola \( y = -\frac{1}{2}x^2 + 8x + 16 \). If there is more than one x-intercept, separate them with commas.
**Input Fields:**
- X-intercept(s): [ ]
- Vertex: [ , ]
**Explanation Button:**
Click this button for a detailed explanation.
**Check Button:**
Click this button to check your solution.
**Note:**
Carefully solve the quadratic equation to find the x-intercepts and use the vertex formula for parabolas, \( x = -\frac{b}{2a} \), to determine the vertex coordinates.
**Example Problem:**
For the example parabola \( y = -\frac{1}{2}x^2 + 8x + 16 \), you will:
1. Solve for when \( y = 0 \) to find the x-intercepts.
2. Use the formula \( x = -\frac{b}{2a} \) to determine the x-coordinate of the vertex and substitute it back into the original equation to find the y-coordinate of the vertex.
Click "Explanation" for detailed steps and "Check" to verify your answers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8175d67d-08a3-43eb-bfb3-8ec86236d575%2F583ec2a9-23d6-4e16-a2c0-d9c62c42aa09%2Fgo9fniq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the x-intercept(s) and the vertex of a parabola**
**Problem Statement:**
Find the x-intercept(s) and the coordinates of the vertex for the parabola \( y = -\frac{1}{2}x^2 + 8x + 16 \). If there is more than one x-intercept, separate them with commas.
**Input Fields:**
- X-intercept(s): [ ]
- Vertex: [ , ]
**Explanation Button:**
Click this button for a detailed explanation.
**Check Button:**
Click this button to check your solution.
**Note:**
Carefully solve the quadratic equation to find the x-intercepts and use the vertex formula for parabolas, \( x = -\frac{b}{2a} \), to determine the vertex coordinates.
**Example Problem:**
For the example parabola \( y = -\frac{1}{2}x^2 + 8x + 16 \), you will:
1. Solve for when \( y = 0 \) to find the x-intercepts.
2. Use the formula \( x = -\frac{b}{2a} \) to determine the x-coordinate of the vertex and substitute it back into the original equation to find the y-coordinate of the vertex.
Click "Explanation" for detailed steps and "Check" to verify your answers.
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