9.7 Graphs of Quadratic Inequalities

p. 548

Forms of Quadratic InequalitiesForms 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 graphingSteps 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)

Steps for Graphing (quickly)Steps for Graphing (quickly)1. Complete the data table to get all 5 points2. Graph the vertex3. Graph all other 4 points4. For < or > use DASHED for ≤ or ≥ use SOLID

line5. Shade the appropriate region (“greater than”

shade above the vertex, “less than” shade below the vertex)

Shade above y Shade below y

Shading

Shade above y Shade below y

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

Graph: y ≤ x2 + 6x – 4* Vertex: (-3,-13)

* Solid Line

* Less than means shade BELOW

x = -5, -4, -3, -2, -1

Graph: y > -x2 + 4x – 3* Vertex: (2, 1)

* Dashed Line

* Greater than means shade ABOVE

x = 0, 1, 2, 3, 4

Graph: y ≥ x2 – 8x + 12* Vertex: (4, -4)

* Solid Line

* Greater than means shade ABOVE

x = 2, 3, 4, 5, 6

Graph: y > -x2 + 4x + 5* Vertex: (2, 9)

* Dashed Line

* Greater than means shade ABOVE

x = 0, 1, 2, 3, 4

Assignment