Exercise 16 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+12x-36 > y

SubstituteII

x= 0, y= 0

- ( 0)^2+12( 0)-36 ? > 0

CalcPow

Calculate power

- (0)+12(0)-36? > 0

ZeroPropMult

Zero Property of Multiplication

0+0-36? > 0

IdPropAdd

Identity Property of Addition

- 36 ≯ 0 *

Step 3

Since (0,0) did not produce a true statement, we will shade the region that does not contain the point. Also, note that we have a strict inequality. Therefore, the parabola will be dashed.