Exercise 3 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+4x+1

SubstituteII

x= 0, y= 0

0? ≥ - ( 0)^2+4( 0)+1

CalcPow

Calculate power

0? ≥ (0)+4(0)+1

ZeroPropMult

Zero Property of Multiplication

0? ≥ 0+0+1

IdPropAdd

Identity Property of Addition

0≥ 1 *

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.