Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 11 - Section 11.1 - Sequences - Exercise Set - Page 640: 48


Refer to the blue graph belpw.

Work Step by Step

RECALL: The graph of the function $f(x) = (x-h)^2+k$: (1) has its center at $(h, k)$ (2) involves the following transformation of the parent function $y=x^2$: (a) vertical shift of $|k|$ units, upward when $k\gt 0$, downward when $k \lt0$; and (b) horizontal shift of $|h|$ units, to the right when $h\gt0$, to the left when $h\lt0$ The given equation has: $h=2$ and $k=1$. Thus, the graph of the given function has its vertex at $(2, 1)$ and involves a 2-unit shift to the right and a 1-unit shift upward of the parent function $y=x^2$. Therefore, to graph the given function, perform the following steps: (1) Graph the parent function $y=x^2$ using a table of values. (Refer to the red graph below.) (2) Shift the red graph 2 units to the right and 1 unit upward. (Refer to the blue graph above.)
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