Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.3 Solve x(squared) + bx + c = 0 - 4.2 Exercises - Mixed Review - Page 258: 89


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Work Step by Step

Given: $y=-(x-3)(x-7)$ $y=-x^2+10x-21$ The coefficients are $a=-1, b=10$, and $c=-21$. Because $a \lt0$, the parabola opens down. Find the vertex: $x=\frac{-b}{2a}=\frac{-(10)}{2.(-1)}=5$ then $y=-(5-3)(5-7)=4$ The vertex is $(5,4)$. Draw the axis of symmetry $x=5$. The y-intercept is $-8$. Plot the point $(0,-21)$. Then reflect this point in the axis of symmetry to plot another point, $(10,-21)$. Evaluate the function for another value of x, such as $x=3$. $y=-(3-3)(3-7)=0$ Plot the point $(3,0)$ and its reflection $(7,0)$ in the axis of symmetry. Draw a parabola through the plotted points.
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