Quadratic inequality

A powerpoint presentation on my lesson, Quadratic Inequality

1. Quadratic Inequalities

2. Activity 1: What Makes Me True? Give the solution/ s of each of the following mathematical sentences. x + 5 > 8 r – 3 = 10 2s + 7 ≥ 21 3t – 2 ≤ 13 12 – 5m = - 8

3. Guide Questions How did you find the solution/ s of each mathematical statements? What mathematical concepts or principles did you apply to come up with the solution/ s ? Which mathematical sentences has only one solution? More than one solution? Describe these sentences.

4. Activity 2: Which are Not Quadratic Equations? x 2 + 9z + 20 = 0 2r 2 < 21 - 9t 2x 2 + 2 = 10x r 2 + 10r ≤ - 16 m 2 = 6m - 7 4x 2 – 25 = 0 15 – 6h 2 = 10 3w 2 + 12w ≥ 0 2s 2 + 7s + 5 >

5. Definition Is an inequality that contains a polynomial of degree 2 and can be written in any of the following forms. ax 2 + bx + c > 0 ax 2 + bx + c ≥ 0 ax 2 + bx + c < 0 ax 2 + bx + c ≤ 0 where a, b , and c are real numbers and a ≠ 0.

6. To solve a quadratic inequality, find the roots of its corresponding equality. Find the solution set of x 2 + 7x + 12 > 0. The corresponding equality of x 2 + 7x + 12 > 0 is x 2 + 7x + 12 = 0. Solve x 2 + 7x + 12 = 0. ( x + 3)(x + 4) = 0 Why? x + 3 = 0 & x + 4 = 0 Why? x = - 3 & x = - 4 Why?

7. Plot the points corresponding to -3 and -4 on the number line. For - ∞ < x < - 4, Let x = - 7 For – 4 < x < - 3, Let x = 3.6 For – 3 < x < ∞, Let x = 0 x 2 + 7x + 12 > 0 (-7) 2 + 7(-7) + 12 > 0 49 – 49 + 12 > 0 12 > 0 (true) x 2 + 7x + 12 > 0 (-3.6) 2 + 7(-3.6) + 12 > 0 12.96 – 25.2 + 12 > 0 -0.24 > 0 (false) x 2 + 7x + 12 > 0 (0) 2 + 7(0) + 12 > 0 0 + 0 + 12 > 0 12 > 0 (true) The three interval are: - ∞ < x < - 4, - 4 < x < - 3, - 3 < x < ∞. Test a number from each interval against the inequality.

8. Also test whether the points x = - 3 and x = - 4 satisfy the equation. x 2 + 7x + 12 > 0 (-3) 2 + 7(-3) + 12 > 0 9 – 21 + 12 > 0 0 > 0 (false) x 2 + 7x + 12 > 0 (-4) 2 + 7(-4) + 12 > 0 16 – 28 + 12 > 0 > 0 (false) Therefore, the inequality is true for any value of x in the interval - ∞ < x < - 4 or 3 < x < ∞ , and these intervals exclude – 3 and – 4. The solution set of the inequality is { x:x < - 4 or x > - 3}.

9. Quadratic Inequalities In Two Variables There are quadratic inequalities that involves two variables. These inequalities can be written in any of the following forms. y > ax 2 + bx + c y ≥ ax 2 + bx + c y < ax 2 + bx + c y ≤ ax 2 + bx + c