This powerpoint presentation discusses or talks about the topic or lesson Quadratic Inequalities. It also discusses and explains the rules, steps and examples of Quadratic Inequalities.

1. Quadratic
Inequalities

2. Quadratic Inequalities
It is an inequality of the form of ax2
+ bx + c (<, >, ≤, ≥) 0, where a, b
and c are real numbers and a ≠ 0

3. Quadratic Inequalities
Example:
x2 + x – 6 = 0
Solution:
The left side of the equation can be
factored

4. Example: x2 + x – 6 = 0
(x + 3) (x-2) > 0
The inequality states that the product of x + 3
and x – 2 is positive. If both factors are positive
or both negative, the product is positive

5. Value Where On the Number Line
x + 3 = 0 If x = -3 Put a 0 above –3
x + 3 > 0 If x > -3 Put + signs to the right of -3
x + 3 < 0 If x < -3 Put – signs to the left of -3
Value Where On the Number Line
x + 2 = 0 If x = -2 Put a 0 above –2
x + 2 > 0 If x > -2 Put + signs to the right of -2
x + 2 < 0 If x < -2 Put – signs to the left of -2

6. x – 2 - - - - - - - - + + + + +
x + 3 - - - 0 + + + + 0 + + + +
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
We can see from the sign graph that the product is positive if x <-3
and also positive if x > 2.
Positive product
since both factors
are negative
Positive product
since both factors
are positive

7. Steps in solving a Quadratic
Inequality with a sign Graph
1. Write the inequality with 0 on the right
side
2. Factor the quadratic trinomial
3. Prepare a sign graph showing where
each factor is positive, negative, or zero
4. Use the rules for multiplying signed
numbers to determine which regions
satisfy the original inequality

8. 3𝑥 − 4
𝑥 − 2
≥ 2
3𝑥 − 3
𝑥 + 4
≤ 0
These inequalities are called Rational
inequalities