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: 29

Answer

Standard form: $y=[x-(-4)]^2-5$ Vertex: $(-4,-5)$ Axis of symmetry: $x=-4$ The x-intercepts are: $(-4+\sqrt 5,0)$ and $(-4-\sqrt 5,0)$
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Work Step by Step

Standard form: $y=a(x-h)^2+k$, in which $(h,k)$ is the vertex. $y=x^2+8x+11$ $y=x^2+2(4)x+4^2-4^2+11$ $y=(x+4)^2-5$ $y=[x-(-4)]^2-5$ Vertex: $(-4,-5)$ Axis of symmetry: $x=-4$ $y=0$ $[x-(-4)]^2-5=0$ $[x-(-4)]^2=5$ $x+4=±\sqrt 5$ $x=-4+\sqrt 5$ or $x=-4-\sqrt 5$ The x-intercepts are: $(-4+\sqrt 5,0)$ and $(-4-\sqrt 5,0)$
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