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Chapter 9: Q. 9.129 (page 972)

(a) Solve 鈭�x2鈭�6x鈭�5>0graphically and (b) write the solution in interval notation.

Short Answer

Expert verified

The solution in interval notation is-5,鈥�-1

Step by step solution

01

Step 1. Given information

鈭�x2鈭�6x鈭�5>0

02

Step 2. Graph the function

鈭�x2鈭�6x鈭�5>0a=-1,b=-6,c=-5

Parabola opens down as ais negative

Axis of symmetry

x=-b2ax=--62-1x=-3

Vertex

fx=鈭�x2鈭�6x鈭�5f-3=鈭�-32鈭�6-3鈭�5f-3=-9+18-5f-3=4

vertex is-3,4

03

Step 3. y-intercept

f0=鈭�02鈭�60鈭�5f0=-5

y-intercept is 0,-5

Point symmetric to y-intercept is 6,12

x-intercept is

fx=-x2-6x-50=-x+1x+5x=-1orx=-5

The x-intercepts are -1,0and-6,0

The graphical solution is

04

Step 4. Solution

The solution in interval notation is鈥�-5,鈥�-1

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