Quadratic Inequalities for 9th grade Philippine students

1. Quadratic
Inequalities
2nd Quarter
9TH GRADE

2. Learning Objectives
At the end of this unit, you should be able to:
identify
quadratic
inequalities;
01
solve
problems
involving
quadratic
inequalities
03
solve
quadratic
inequalities;
and
02
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3. What is a
Quadratic
Inequality?
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4. A quadratic
inequality (in
one variable) is
an inequality
with one
unknown
(usually ) of
degree 2.
Simply put, it is
like a quadratic
equation but the
equal sign is
replaced by a
less than, greater
than, at most, or
at least symbol.
9TH GRADE

5. It can be written in the following forms:
𝑎𝑥2
+ 𝑏𝑥 + 𝑐 > 𝟎
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where and are
real numbers,
and a ≠ 0
𝒂𝒙𝟐
+ 𝒃𝒙 + 𝒄 < 𝟎
𝒂𝒙𝟐
+ 𝒃𝒙 + 𝒄 ≥ 𝟎
𝒂𝒙𝟐
+ 𝒃𝒙 + 𝒄 ≤ 𝟎

6. Quadratic vs
Linear Inequality
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7. If the simplified
form of an
inequality
doesn’t have 2 as
the highest
power of the
variable x, it is
not a quadratic
inequality.
Things to remember about quadratic
inequalities:
When
simplified,
quadratic
inequalities
retain 2 as the
highest power
of the variable
x.
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The difference
between a
quadratic
equation and a
quadratic
inequality is that
the equation is
equal to some
number while
inequality is
either less than
or greater than

8. Critical Values,
Test Intervals,
and Test
Numbers
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9. Insert your multimedia content here
Watch
the
Video
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10. Solving
Quadratic
Inequalities
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11. Solve the quadratic inequality 𝒙𝟐 + 𝒙 > 𝟔
Step 1: Write one side of the inequality
in the form and the other side zero.
𝑥2
+ 𝑥 > 6
𝑥2
+ 𝑥 − 6 > 0

12. Step 2: Treat the inequality as a
quadratic equation. Solve the
equation. The solutions are the critical
numbers of the inequality.
𝑥2
+ 𝑥 − 𝑏 = 0
𝑥 + 3 𝑥 − 2 = 0

13. Step 3: Use the critical
numbers to determine
the test intervals. The
test intervals are 𝑥 <
− 3, −3 < 𝑥 < 2, 𝑥 > 2

14. Step 4: Choose one test number in each
test interval and evaluate the inequality at
that value. You may use the original
inequality or factored form of the inequality
when evaluating.
Original Inequality: 𝑥2
+ 𝑥 > 6
Factored Inequality: 𝑥 + 3 𝑥 − 2 > 0

15. Step 4:
Test Interval Test Number Evaluation Conclusion
𝑥 < −3 𝑥 = −4
−4 2
+ −4 > 6
16 − 4 > 6
12 > 6
True
−3 < 𝑥 < 2 𝑥 = 0 0 2 + 0 > 6
0 > 6
False
𝑥 > 2 𝑥 = 3
3 2
+ 3 > 6
9 + 3 > 6
12 > 6
True
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16. CREDITS: This presentation template was created
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infographics & images by Freepik.
Thanks!
9TH GRADE