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Identify the graph of y=-4x2+8x+2. Then identify the vertex and axis of symmetry.

Identify the graph of y=-4x2+8x+2. Then identify the vertex and axis of symmetry.

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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Identify the graph of y=-4x2+8x+2. Then identify the vertex and axis of symmetry.

The image contains four graphs of quadratic functions, each on a grid with labeled axes. **Graph Descriptions:** 1. **Top Left Graph:** - This graph depicts a downward-opening parabola. - The vertex of the parabola is located at the point (0, 6). - The y-intercept is at (0, 6). - The parabola symmetrically extends downwards, crossing the x-axis at approximately x = -2 and x = 2. 2. **Top Right Graph:** - It shows a similar downward-opening parabola. - The vertex is at the point (0, 8). - The y-intercept is at (0, 8). - The parabola crosses the x-axis around x = -√8 and x = √8. 3. **Bottom Left Graph:** - Another downward-opening parabola is presented. - The vertex is at the point (0, 4). - The y-intercept is at (0, 4). - It intersects the x-axis around x = -2 and x = 2. 4. **Bottom Right Graph:** - This graph also features a downward-opening parabola. - The vertex is at the point (0, 2). - The y-intercept is (0, 2). - It crosses the x-axis approximately at x = -√2 and x = √2. **Common Features:** - All graphs exhibit parabolas that open downwards, demonstrating a negative leading coefficient. - The axis of symmetry for all parabolas is the y-axis, meaning they are symmetrical around the vertical line x = 0. These graphs illustrate various quadratic functions with different vertex points but similar structures, showing the transformation of a basic parabola as the vertex shifts.
Transcribed Image Text:The image contains four graphs of quadratic functions, each on a grid with labeled axes. **Graph Descriptions:** 1. **Top Left Graph:** - This graph depicts a downward-opening parabola. - The vertex of the parabola is located at the point (0, 6). - The y-intercept is at (0, 6). - The parabola symmetrically extends downwards, crossing the x-axis at approximately x = -2 and x = 2. 2. **Top Right Graph:** - It shows a similar downward-opening parabola. - The vertex is at the point (0, 8). - The y-intercept is at (0, 8). - The parabola crosses the x-axis around x = -√8 and x = √8. 3. **Bottom Left Graph:** - Another downward-opening parabola is presented. - The vertex is at the point (0, 4). - The y-intercept is at (0, 4). - It intersects the x-axis around x = -2 and x = 2. 4. **Bottom Right Graph:** - This graph also features a downward-opening parabola. - The vertex is at the point (0, 2). - The y-intercept is (0, 2). - It crosses the x-axis approximately at x = -√2 and x = √2. **Common Features:** - All graphs exhibit parabolas that open downwards, demonstrating a negative leading coefficient. - The axis of symmetry for all parabolas is the y-axis, meaning they are symmetrical around the vertical line x = 0. These graphs illustrate various quadratic functions with different vertex points but similar structures, showing the transformation of a basic parabola as the vertex shifts.
Expert Solution
Step 1: Define the problem.

To identify the graph of straight y equals negative 4 straight x squared plus 8 straight x plus 2.

 Then, to identify the vertex and axis of symmetry.

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