3.9 Graphs of Quadratic Inequalitiesp. 96-101

Forms of Quadratic Inequalitiesy<ax2+bx+c y>ax2+bx+cy≤ax2+bx+c y≥ax2+bx+c

Graphs will look like a parabola with a solid or dotted line and a shaded section.

The graph could be shaded inside the parabola or outside.

Steps for graphing1. Sketch the parabola y=ax2+bx+c.

(dotted line for < or >, solid line for ≤ or ≥)

** remember to use 5 points for the graph!

2. Choose a test point and see whether it is a solution of the inequality.

3. Shade the appropriate region.

(if the point is a solution, shade where the point is, if it’s not a solution, shade the other region)

Example:Graph y ≤ x2+6x- 4

3)1(2

6

2

a

bx

* Vertex: (-3,-13)

* Opens up, solid line

134189

4)3(6)3( 2

y 9- 5-

12- 4-

13- 3-

12- 2-

9- 1-

yx

• Test Point: (0,0)

0≤02+6(0)-4

0≤-4 So, shade where the point is NOT!

Test point

Graph: y>-x2+4x-3

* Opens down, dotted line.

* Vertex: (2,1)

2)1(2

4

2

a

bx

1384

3)2(4)2(1 2

y

y

* Test point (0,0)

0>-02+4(0)-3

0>-3

x y

0 -3

1 0

2 1

3 0

4 -3

Test Point

Page 98 #5-10, 11-16

Page 99 # 34-36

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