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6.7 Graphing and Solving Quadratic Inequalities

6.7 Graphing and Solving Quadratic Inequalities. 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. Solving by Graphing.

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6.7 Graphing and Solving Quadratic Inequalities

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  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 x = 3 ; x = 1 Is the Graph up or Down?

  8. Solve x2 - 4x + 3 > 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 > 0 True Let x = 4 42 – 4(4) + 3 > 0 True Let x = 2 22 – 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 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

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