Algebra 2 Graphs of Quadratic Inequalities

Integrated 2 4-1 Graphing

Quadratic Functions 2

Algebra 2 Bell Ringer

Use the function

A. Tell whether the graph opens up or down.

B. Tell whether the vertex is a maximum or a

minimum.

C. Find an equation for the line of symmetry.

D. Find the coordinates of the vertex.

23 18 25y x x

Daily Learning Target (DLT):

Wednesday January 9, 2013

“I can understand, apply, and

remember how to graph parabola

inequalities by finding the vertex

and a test point for shading.”

Integrated 2 4-1 Graphing

Quadratic Functions 4

Algebra 2 Bell Ringer

Use the function

A. Tell whether the graph opens up or down.

UP

B. Tell whether the vertex is a maximum or a

minimum. MINIMUM

C. Find an equation for the line of symmetry. x = 3

D. Find the coordinates of the vertex. (3,-2)

23 18 25y x x

5

Algebra 2 Assignment – Front Side

1. Vertex: (-8,0)

2. Vertex: (1,-4)

3. Vertex: (9,6)

4. Vertex: (2,2)

5. Vertex: (1,-4)

6. Vertex: (-3,-1)

7. Vertex: (4,-4) , Max = -4

8. Vertex: (2,-4), Max = -4

6

Algebra 2 Assignment – Back Side

9. Vertex: (-1,-2)

10. Vertex: (-5, -5)

11. Vertex: (9,-2), Axis of Symmetry: x = 9,

Min. Value: y = -2

12. Vertex: (9,5), Axis of Symmetry: x = 9,

Min. Value: y = 5

13. Vertex: (6,6), Axis of Symmetry: x = 6,

Max. Value: y = 6

7

Algebra 2 Assignment – Back Side

14. Vertex: (-5,4), Axis of Symmetry: x = -5,

Max. Value: y = 4

15. Vertex: (0,7), Axis of Symmetry: x = 0,

Max. Value: y = 7

16. Vertex: (6,8), Axis of Symmetry: x = 6,

Min. Value: y = 8

17. Vertex: (2,8), Axis of Symmetry: x = 2,

Min. Value: y = 8

18. Vertex: (-2,1), Axis of Symmetry: x = -2,

Min. Value: y = 1

Forms of Quadratic Inequalities y<ax2+bx+c - Dashed y>ax2+bx+c - Dashed y≤ax2+bx+c - Solid y≥ax2+bx+c - Solid

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 graphing

1. 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 such as (0,0).

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 1: Graph y ≤ x2+6x- 4

Example 1: 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

Example 2: Graph y>-x2+4x-3

Example 2 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

Last Example! Sketch the intersection of the given inequalities. 1 y≥x2 and 2 y≤-x2+2x+4

Graph both on the same coordinate plane. The place where the shadings overlap is the solution.

Vertex of #1: (0,0)

Other points: (-2,4), (-1,1), (1,1), (2,4)

Vertex of #2: (1,5)

Other points: (-1,1), (0,4), (2,4), (3,1)

* Test point (1,0): doesn’t work in #1, works in #2.

SOLUTION!

Assignment

Work on your X-Y Table and Graphing Parabola Inequalities Worksheet

Integrated 2 4-1 Graphing

Quadratic Functions 16

Exit Quiz – 5 Points

Use the function

A. Tell whether the graph opens up or down.

B. Tell whether the vertex is a maximum or a

minimum.

C. Find an equation for the line of symmetry.

D. Find the coordinates of the vertex.

22 3 1y x x