5.7 graphs of quadratic inequalities
TRANSCRIPT
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