Exercise 41 Page 219

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+10x-4

SubstituteII

x= 0, y= 0

0? ≤ ( 0)^2+10( 0)-4

CalcPow

Calculate power

0? ≤ 0+10(0)-4

ZeroPropMult

Zero Property of Multiplication

0? ≤ 0+0-4

IdPropAdd

Identity Property of Addition

0≤ - 4 *

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 the inequality is not strict. Therefore, the parabola will be solid.