Exercise 38 Page 219

Since we have a strict inequality, the parabola will be a dashed line.

Practice makes perfect

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

Graph the related quadratic function.
Test a point not on the parabola.
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

Let's draw the graph of the related function, y=x^2+5x+4.

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+5x+4

SubstituteII

x= 0, y= 0

0 ? ≥ ( 0)^2+5( 0)+4

CalcPow

Calculate power

0 ? ≥ 0+5(0)+4

ZeroPropMult

Zero Property of Multiplication

0 ? ≥ 0+0+4

IdPropAdd

Identity Property of Addition

0 ≥ 4 *

Step 3

Since (0,0) produced a false statement, we will shade the region that does not contain the point. Notice that the inequality is not strict. Therefore, the parabola will be solid.

Subchapter links

1 Solving Quadratic Equations by Factoring p.217

2 Complex Numbers p.217

3 The Quadratic Formula and the Discriminant p.218

4 Transformations of Quadratic Graphs p.218

5 Quadratic Inequalities p.219

Practice Test p.219

Exercise 38 Page 219

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