1. 4.9 Notes – Graph and Solve Quadratic Inequalities

2. y = ax2 + bx +c
y > ax2 + bx +c
Don’t shade!
Shade up

3. y < ax2 + bx +c
Shade down

4. Test Point
A test point in the area you think you should shade. If you plug it in and it works, then shade that area

5. 1. Sketch the graph of the quadratic inequality using the vertex and intercepts. Then choose a test point and verify your solution.
(1,4)
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = 1
y = 4

6. x = 1 y = 4 3, -1 3 (1,4) x -3 x 1 -3x + x -(x – 3)(x + 1) = 0
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = 1 x -3 x 1
y = 4
-3x + x
3, -1
-(x – 3)(x + 1) = 0 3
x – 3 = 0 or
x + 1 = 0
x = 3
x = -1

7. x = 1 y = 4 3 (1,4) 3, -1 Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = 1
y = 4
3, -1 3

8. Test Point:
(0, 0)
Solution

9. 1. Sketch the graph of the quadratic inequality using the vertex and intercepts. Then choose a test point and verify your solution.
(-2, -9)
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = -2
y = -9

10. x = -2 y = -9 (-2, -9) x 5 x -1 5x + -x (x + 5)(x – 1) = 0 –5, 1
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________ x 5
x = -2 x -1 5x + -x
y = -9
(x + 5)(x – 1) = 0
–5, 1
x + 5 = 0 or
x – 1 = 0 –5
x = –5
x = 1

11. y = -9 (-2, -9) x = -2 –5, 1 –5 Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = -2
y = -9
–5, 1 –5

12. Test Point:
(0, 0)
Solution

13. 1. Sketch the graph of the quadratic inequality using the vertex and intercepts. Then choose a test point and verify your solution.
(-2, -2)
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = -2
y = -2

14. 2 2 2 x = -2 2(x2 + 4x + 3) = 0 y = -2 (-2, -2) x 3 x 1 5x + -x –3, –1
Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = -2
2(x2 + 4x + 3) = 0 x 3
y = -2 x 1 5x + -x
–3, –1
2(x + 3)(x + 1) = 0 6
x + 3 = 0 or
x + 1 = 0
x = –3
x = -1

15. y = -2 (-2, -2) x = -2 –3, –1 6 Vertex: ________________
axis of symmetry: ________
circle one: min or max
min/max value: _________
x – intercept(s): _________
y-intercept: _____________
x = -2
y = -2
–3, –1 6

16. Test Point:
(0, 0)
Solution

17. 2. Sketch the graph of the quadratic inequality using a table
2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution.

18. 2. Sketch the graph of the quadratic inequality using a table
2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution. x
(x,y)
(0, 3)
(–1, –3) –1
(–2, –5) –2 –3
(–3, –3) –4
(–4, 3)

19. (0, 3)
(–1, –3)
(–2, –5)
(–3, –3)
(–4, 3)

20. Test Point:
(1, 1)
Not a Solution

21. 2. Sketch the graph of the quadratic inequality using a table
2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution.

22. 2. Sketch the graph of the quadratic inequality using a table
2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution. x
(x,y)
(4, 1) 4
(3, 4) 3
(2, 5) 2 1
(1, 4)
(0, 1)

23. (4, 1)
(3, 4)
(2, 5)
(1, 4)
(0, 1)

24. Test Point:
(1, 1)
Not a Solution

25. 2. Sketch the graph of the quadratic inequality using a table
2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution.

26. 2. Sketch the graph of the quadratic inequality using a table
2. Sketch the graph of the quadratic inequality using a table. Then choose a test point and verify your solution. x
(x,y)
(4, -3) 4
(2, 3) 2
(0, 5) -2
(-2, 3) -4
(-4, -3)

27. (4, -3)
(2, 3)
(0, 5)
(-2, 3)
(-4, -3)

28. Test Point:
(0, 0)
Solution