## Algebra 1

Published by Prentice Hall

# Chapter 9 - Quadratic Functions and Equations - 9-2 Quadratic Functions - Practice and Problem-Solving Exercises - Page 545: 21

#### Answer

Axis of symmetry: x=2 Vertex: (2, 17) The graph is shown below: #### Work Step by Step

$y = -2x^{2} + 8x + 9$ The standard form for a quadratic equation is $y = ax^{2} + bx + c$ So a= -2, b= 8, and c= 9 Axis of symmetry: The formula for axis of symmetry is $x= \frac{-b}{2a}$ $x= \frac{-(8)}{2(-2)}$ $x= \frac{-8}{-4}$ x=2 Vertex: Plug in the x value of the axis of symmetry to find the y value of the vertex. $y = -2x^{2} + 8x + 9$ $y = -2(2)^{2} + 8(2) + 9$ y= -8 + 16 + 9 y= 17 The vertex is (2, 17) We plot the vertex on the graph. Since the a value is -2 and is negative the parabola opens downwards. So we graph a parabola starting from the vertex opening downwards.

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