Mrs. Evany B. Colobong
At the end of the session, the
students should be able to:
a. Write a quadratic equation in standard
form;
b. Identify quadratic equations; and
c. Appreciate the importance of quadratic
equations.
Product of
𝑚
𝑛
Powers
𝑎 ∙ 𝑎 = 𝑎𝑚+𝑛
Powers of
𝑚
Quotient
𝑚
Powers
of Powers
𝑎𝑏
Product
= 𝑎𝑚 𝑏𝑚
of Quotient
𝑛
𝑛
𝑎
𝑎
𝑎
𝑚−𝑛
=
𝑎
= 𝑛
𝑛
𝑎
𝑏
𝑏
Power of Powers
𝑚 𝑛
𝑚𝑛
(𝑎 ) = 𝑎
Simplify the following.
1.
2.
3.
4.
5.
4
6
∙𝑥
2 3
𝑥
=
4 5
3𝑎 𝑏 ∙ 4𝑎 𝑏 =
3
2
𝑚 𝑛
=
𝑚𝑛
2 5
𝑎 𝑏 =
2
3
3𝑥 𝑦
𝑧5
3
=
Solve for the product of the
following.
1.
2.
3.
4.
5.
2
3(𝑥 + 7)
2𝑠(𝑠 − 4)
2
3 − 4𝑚
(𝑥 + 9)(𝑥 − 2)
(2𝑡 − 1)(𝑡 + 5)
𝟐
𝟐
𝒙 − 𝟓𝒙 + 𝟑 = 𝟎
𝒓 = 𝟏𝟒𝟒
𝟗 − 𝟒𝒙 = 𝟏𝟓
𝟐𝒔 + 𝟑𝒕 = −𝟕
𝟐
𝟐
𝒕 − 𝟕𝒕 + 𝟔
𝟗𝒓 − 𝟐𝟓 = 𝟎
𝒄 = 𝟏𝟐𝒏 − 𝟓
𝟖𝒌 − 𝟑 = 𝟏𝟐
Which of the following is a linear equation?
𝟐
𝒙 − 𝟓𝒙 + 𝟑 = 𝟎
𝟐
𝒕 − 𝟕𝒕 + 𝟔
𝟐
𝒓 = 𝟏𝟒𝟒
𝟐
𝟗𝒓 − 𝟐𝟓 = 𝟎
QUADRATIC EQUATIONS
A
Quadratic Equation in One
Variable
is
a
mathematical
sentence of degree 2 that can be
written in the following standard
2
form 𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0, where 𝑎, 𝑏
and 𝑐 are real numbers and 𝑎 ≠ 0.
In
2
𝑎𝑥
the equation,
is the
quadratic term, 𝑏𝑥 is the linear
term, and 𝑐 is the constant term.
Examples:
2
 2𝑥 − 6𝑥 − 15 = 0
 2𝑥 𝑥 − 4 = 18
 𝑥−3 𝑥+1 =4
QUADRATIC
EQUATION
VALUES
STANDARD FORM OF 𝒂, 𝒃
and 𝒄
𝒂=𝟐
𝟐𝒙𝟐 − 𝟔𝒙 − 𝟏𝟓 = 𝟎 𝟐𝒙𝟐 − 𝟔𝒙 − 𝟏𝟓 = 𝟎 𝒃 = −𝟔
𝒄 = −𝟏𝟓
𝒂=𝟐
𝟐𝒙 𝒙 − 𝟒 = 𝟏𝟖
𝟐𝒙𝟐 − 𝟖𝒙 − 𝟏𝟖 = 𝟎 𝒃 = −8
𝒄 = −𝟏8
𝒂=𝟏
𝒙 − 𝟑 𝒙 + 𝟏 = 𝟒 𝒙𝟐 − 𝟐𝒙 − 𝟕 = 𝟎 𝒃 = −𝟐
𝒄 = −𝟕
QUADRATIC
TERM
LINEAR
TERM
CONSTANT
TERM
𝟐𝒙𝟐
−𝟔𝒙
−𝟏𝟓
𝟐𝒙𝟐
−𝟖𝒙
−𝟏𝟖
𝒙𝟐
−𝟐𝒙
−𝟕
Tell whether each equation is QUARATIC or
NOT QUADRATIC.
1.
2.
3.
4.
5.
2
𝑥
+ 7𝑥 + 12 = 0
−3𝑥 𝑥 + 5 = 0
12 − 4𝑥 = 0
𝑥 + 7 𝑥 − 7 = 3𝑥
2𝑥 + 𝑥 + 4 = 𝑥 − 3 + (𝑥 − 3)
Write each equation in standard form then
identify the values of 𝑎, 𝑏 and 𝑐.
1.
2.
3.
4.
5.
2
2𝑥
+ 5𝑥 − 3 = 0
2
3 − 2𝑥 = 7
𝑥 4𝑥 + 6 = 28
3𝑥 − 7 5𝑥 + 2 = 0
2
−3𝑥 + 5𝑥 = 7