6.7 Graphing and Solving Quadratic Inequalities

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 gt x2 -3x 2
Why is it a dotted line?
7
Solve x2 - 4x 3 gt 0

• Find the zeros, (x - 3)(x 1) 0
• x 3 x 1
• Is the Graph up or Down?

8
Solve x2 - 4x 3 gt 0

• Find the zeros, (x - 3)(x 1) 0
• x 3 x 1
• 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 02 - 4(0) 3 gt 0 True
• Let x 4 42 4(4) 3 gt 0 True
• Let x 2 22 4(2) 3 gt 0 False
• Only shade where it is true.

11
Solve x2 - 4x 3 gt 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 1 -2 x 1
• Let x 0
• (0)2 (0) 2 0 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) 2 4 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