Exercise 2 Page 210

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.

y> x^2+6x-2

SubstituteII

x= 0, y= 0

0? > ( 0)^2+6( 0)-2

CalcPow

Calculate power

0? > 0+6(0)-2

ZeroPropMult

Zero Property of Multiplication

0? > 0+0-2

IdPropAdd

Identity Property of Addition

0> - 2 ✓

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.