College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.6 - Transformations of Functions - 2.6 Exercises - Page 243: 34


Refer to the blue graph below.

Work Step by Step

RECALL: The function $y=f(x-h)$ involves a horizontal shift of $h$ units to the right of the parent function when $h\gt 0$ and $|h|$ units to the left when $h \lt 0$. The given function can be written as $f(x)=[x-(-1)]^2$. This is in the same format as the equation above, and has $h=-1$. This means that the graph of $y=(x+1)^2$ involves a horizontal shift of $|-1|=1$ unit to the left of the parent function $y=x^2$ Thus, to graph the given function: (1) Graph the parent function $y=x^2$ . (Refer to the red graph in the attached image below) (2) Shift the parent function 1 unit to the left. (Refer to the blue graph in the attached image above.)
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