College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 2 - Section 2.7 - Graphing Techniques - 2.7 Exercises - Page 255: 55

Answer

See the picture below.
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Work Step by Step

By calculating the values of $f(x)=(x+2)^2$ (with blue) and $g(x)=x^2$ (with red) we can see that for every corresponding $f(x)$ and $g(x)$ value, each x value of $g(x)$ is 2 less than the x value of $f(x)$. For drawing the exact parent graph, here is the table of values: $g(-2)= -2^2=4$ $g(-1)= -1^2=1$ $g(0)= 0^2=0$ $g(1)= 1^2=1$ $g(2)=2^2=4$ Therefore the graph of $f(x)$ is exactly the same as the graph of $g(x)=x^2$ but translated 2 units left. Meaning, that the transformation involves a horizontal shift to the left by $2$. For drawing the exact graph of $f(x)$ here is the table of values of the given function: $f(-4)=(-4+2)^2=4$ $f(-3)=(-3+2)^2=1$ $f(-2)=(-2+2)^2=0$ $f(-1)=(-1+2)^2=1$ $f(0)=(0+2)^2=4$
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