Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.2 - Graphs of Functions - 2.2 Exercises - Page 167: 29

Answer

When you graph using the windows suggested in part "c" and "d" you will see that "d" makes the graph too flat. Answer "c" is the best choice.

Work Step by Step

f(x) = -x^{2} + 8x f(x) = -(x^{2} - 8x + ?) f(x) = -(x^{2} - 8x + 16) + 16 f(x) = -(x - 4)^{2} + 16 Start by finding the vertex of the graph. I used completing the square method to see the vertex is (4, 16). (You could also use the method where the x-coordinate of the vertex equals (-b/2a). Then substitute the x value into the function to find the y - coordinate. You still get the same result for the vertex.) Right away you know the windows shown in parts (a) and (b) will not work as they are not large enough to show the vertex in the graphing window (neither goes up to 16 on y).
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