Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 3 - 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 248: 30

Answer

Standard form: $y=[x-(-5)]^2-11$ Vertex: $(-5,-11)$ Axis of symmetry: $x=-5$ The x-intercepts are: $(-5+\sqrt {11},0)$ and $(-5-\sqrt {11},0)$
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Work Step by Step

Standard form: $y=a(x-h)^2+k$, in which $(h,k)$ is the vertex. $y=x^2+10x+14$ $y=x^2+2(5)x+5^2-5^2+14$ $y=(x+5)^2-11$ $y=[x-(-5)]^2-11$ Vertex: $(-5,-11)$ Axis of symmetry: $x=-5$ $y=0$ $[x-(-5)]^2-11=0$ $[x-(-5)]^2=11$ $x+5=±\sqrt {11}$ $x=-5+\sqrt {11}$ or $x=-5-\sqrt {11}$ The x-intercepts are: $(-5+\sqrt {11},0)$ and $(-5-\sqrt {11},0)$
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