For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!  https://tinyurl.com/y9muob6q LIKE and FOLLOW me here!  https://tinyurl.com/ycjp8r7u https://tinyurl.com/ybo27k2u References: Nivera, G. C. (2013), Grade 9 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines. Mathematics Grade 9 Learner's Material (2014). Department of Education Oronce, O. A. (2019). E-math Worktext in Mathematics 9. Rex Book Store, Inc. Manila, Philippines

1. Grade 9 – Mathematics
Quarter I
ILLUSTRATING QUADRATIC
INEQUALITIES

2. Objective:
•illustrate quadratic inequalities.

3. 𝑥2 + 9𝑥 + 20 = 0
2𝑠2
+ 7𝑠 + 5 > 0
2𝑡2 < 21 − 9𝑡
15 − 6ℎ2
= 100
Which are not Quadratic Equations?
𝑟2 + 10𝑟 ≤ −16
4𝑥2
− 25 = 0
3𝑤2 + 12𝑤 ≥ 0
𝑚2
= 6𝑚 − 7

4. A quadratic inequality 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.

5. Determine whether each mathematical sentence
is a quadratic inequality or not.
𝑥2
+ 9𝑥 + 14 > 0
Quadratic Inequality, because it has a degree of 2,
𝑎 ≠ 0, and written in the form of 𝑎𝑥2
+ 𝑏𝑥 + 𝑐 > 0.
3𝑥2
− 4𝑥 = 1
Not a Quadratic Inequality, the
mathematical sentence is a quadratic equation.

6. Determine whether each mathematical sentence
is a quadratic inequality or not.
Quadratic Inequality
2𝑥 − 3 𝑥 + 2 > 0
2𝑥2
+ 𝑥 − 6 > 0
3𝑥2
+ 18 < 3 𝑥2
− 4𝑥
3𝑥2
+ 18 < 3𝑥2
− 12𝑥
3𝑥2
− 3𝑥2
+ 12𝑥 + 18 < 0
12𝑥 + 18 < 0
Not a Quadratic Inequality

7. Test Yourself!
Determine whether each mathematical sentence is a quadratic
inequality or not.
1. 15 − 2𝑥 = 3𝑥2
2. 3𝑥2
+ 8 + 𝑥 + 6 ≥ −4
3. 𝑥2
− 4 < 𝑥2
− 2𝑥
4. 12 − 5𝑥 + 𝑥3
≥ 0
5. 2 + 𝑥2
− 𝑥 < 0
Quadratic Inequality
Not
Not
Not
Quadratic Inequality