1. 6.7 Graphing and Solving Quadratic Inequalities

2. Solving by Graphing
Find the Vertex and the zeros of the Quadratic Equation
You can find the zero in anyway we used in this chapter. Making Table
Factoring
Completing the Square
Quadratic Formula

3. Solving by Graphing
Given: Zeros:

4. Solving by Graphing
Given: Zeros:
y = x 2 -3x +2

5. Solving by Graphing Which way do I shade?, inside or outside
y = x 2 -3x +2

6. Solving by Graphing The answers are in the shaded area
y > x2 -3x +2
Why is it a
dotted line?

7. Solve x2 - 4x + 3 > 0 Find the zeros, (x - 3)(x – 1) = 0
Is the Graph up or Down?

8. Solve x2 - 4x + 3 > 0 Find the zeros, (x - 3)(x – 1) = 0
Where do we shade? Inside or Outside

9. Try a few points
One lower then the lowest zero, one higher then the highest zero and one in the middle.
Let x =0
Let x = 4
Let x = 2

10. Try a few points
One lower then the lowest zero, one higher then the highest zero and one in the middle.
Let x = (0) + 3 > 0 True
Let x = – 4(4) + 3 > 0 True
Let x = – 4(2) + 3 > 0 False
Only shade where it is true.

11. Solve x2 - 4x + 3 > 0

12. Solve Quadratic Inequalities Algebraically

13. Break the number line into three parts
Test a number less then -2 x ≤ -2
Let x = - 3
(-3)2 + ( -3) ≤ 2 9 – 3 = 6
6 is not less then – 2 False

14. Break the number line into three parts
Test a number between -2 and ≤ x ≤ 1
Let x = 0
(0)2 + (0) ≤ = 0
0 is less then 2 True

15. Break the number line into three parts
Test a number great then 1 x ≥ 1
Let x = 2
(2)2 + (2) ≤ = 6
6 is not less then – 2 False

16. Break the number line into three parts
So the answer is -2 ≤ x ≤ 1

17. Homework
Page 333 – 334
# 14, 17, 20, 23,
30, 33, 36, 37, 41

18. Homework
Page 333 – 334
# 15, 18, 21, 24,
31, 34, 37, 38 40