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Chapter 9: Q 9.130 (page 972)

(a) Solve 鈭�x2+10x鈭�16鈮�0graphically and (b) write the solution in interval notation.

Short Answer

Expert verified

The solution in interval notation is(-鈭�鈥�,鈥�2]鈭�鈥�[8,鈥�鈭�鈥�)

Step by step solution

01

Step 1. Given information

鈭�x2+10x鈭�16鈮�0

02

Step 2. Graph the function

鈭�x2+10x鈭�16鈮�0a=-1,b=10,c=-16

Parabola opens down as ais negative

Axis of symmetry

x=-b2ax=-102-1x=5

Vertex

fx=-x2+10x-16f5=-52+105-16f5=9

vertex5,9

03

Step 3. Y-intercept

f0=-02+100-16f0=-16

y-intercept is 0,-16
Point symmetric to y-intercept is 10,16

x-intercept

fx=-x2+10x-160=-x2+10x-160=-x-2x-8x=2orx=8

The x-intercept is 2,0and8,0

04

Step 4. Solutions

The solution in interval notation is(-鈭�鈥�,鈥�2]鈭�鈥�[8,鈥�鈭�鈥�)

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