Exercise 14 Page 211

To graph the quadratic inequality, we will follow three steps.

1. Graph the related quadratic function.
2. Test a point not on the parabola.
3. Shade accordingly. If the point satisfies the inequality, we shade the region that contains the point. If not, we shade the opposite region.

Step 1

Step 2

Next, let's determine which region to shade by testing a point. For simplicity, we will use (0,0) as our test point. Let's see if it satisfies the given inequality.

x^2-2x-8 < y

SubstituteII

x= 0, y= 0

( 0)^2-2 ( 0)-8 ? < 0

CalcPow

Calculate power

0-2(0)-8? < 0

ZeroPropMult

Zero Property of Multiplication

0-0-8 ? < 0

IdPropAdd

Identity Property of Addition

-8 < 0 ✓

Step 3

Since (0,0) produced a true statement, we will shade the region that contains the point. Also, note that we have a strict inequality. Therefore, the parabola will be dashed.