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Chapter 9: Q 370 (page 977)

In the following exercises, 鈸� solve graphically and 鈸� write the solution in interval notation -x2+2x+15>0

Short Answer

Expert verified

The solution in interval notation is鈥�-3,鈥�5

Step by step solution

01

Step 1. Given information

-x2+2x+15>0

02

Step 2. Solve graphically

The quadratic equation is in standard form.

-x2+2x+15>0

Graph the function fx=-x2+2x+15

The parabola opens downward.

Find the line of symmetry

x=-b2ax=1

Find the vertex

fx=-x2+2x+15f1=18

vertex is 1,18

Find the x-intercepts. Let fx=0

fx=-x2+2x+150=-x+3x-5x=-3andx=5

The x-intercepts are -3,0and5,0

The graph of the parabola is

03

Step 3. Solution

The solution in interval notation is-3,鈥�5

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