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.
1. x + 5 > 8
2. r – 3 = 10
3. 2s + 7 ≥ 21
4. 3t – 2 ≤ 13
5. 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?
x2 + 9z + 20 = 0 2r2 < 21 - 9t 2x2 + 2 = 10x
r2 + 10r ≤ - 16 m2 = 6m - 7 4x2 – 25 = 0
15 – 6h2 = 10 3w2 + 12w ≥ 0 2s2 + 7s + 5 > 0

5. Definition
 Is an inequality that contains a polynomial of degree 2 and
can be written in any of the following forms.
ax2 + bx + c > 0 ax2 + bx + c ≥ 0
ax2 + bx + c < 0 ax2 + 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 x2 + 7x + 12 > 0.
The corresponding equality of x2 + 7x + 12 > 0 is
x2 + 7x + 12 = 0.
Solve x2 + 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.
The three interval are: - ∞ < x < - 4, - 4 < x < - 3, - 3 < x < ∞.
Test a number from each interval against the inequality.
For - ∞ < x < - 4,
Let x = - 7
For – 4 < x < - 3,
Let x = 3.6
For – 3 < x < ∞,
Let x = 0
x2 + 7x + 12 > 0
(-7)2 + 7(-7) + 12 > 0
49 – 49 + 12 > 0
12 > 0 (true)
x2 + 7x + 12 > 0
(-3.6)2 + 7(-3.6) + 12 > 0
12.96 – 25.2 + 12 > 0
-0.24 > 0 (false)
x2 + 7x + 12 > 0
(0)2 + 7(0) + 12 > 0
0 + 0 + 12 > 0
12 > 0 (true)

8.  Also test whether the points x = - 3 and x = - 4 satisfy the
equation.
x2 + 7x + 12 > 0
(-3)2 + 7(-3) + 12 > 0
9 – 21 + 12 > 0
0 > 0 (false)
x2 + 7x + 12 > 0
(-4)2 + 7(-4) + 12 > 0
16 – 28 + 12 > 0
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 > ax2 + bx + c y ≥ ax2 + bx + c
y < ax2 + bx + c y ≤ ax2 + bx + c