Lesson 1 - Illustrating Quadratic Equation

MA. CATHERINE A.

TIANGCO

LESSON 1:

Illustrates quadratic

equations

Write a quadratic

equation in standard form

Identify quadratic

equations

1. 3(𝑥2+ 7) = 3𝑥2+ 7𝑥
2. 2𝑠(𝑠 − 4) = 2𝑠2− 8𝑠
3. (𝑤 + 7)(𝑤 + 3)= 𝑤2+ 10𝑤 + 21
4. (𝑥 + 9)(𝑥 − 2) = 𝑥2+ 7𝑥 − 18
5.

2𝑡 − 1

𝑡 + 5 = 2𝑡2+ 9𝑡 − 5

6.

𝑥 + 4

𝑥 + 4 = 𝑥2+ 8𝑥 + 16

7.

2𝑟 − 5

2𝑟 − 5 = 4𝑟2− 20𝑟 + 25

8. (3 − 4𝑚)2= 16𝑚2− 24𝑚 + 9
9.

2ℎ + 7

2ℎ − 7 = 4ℎ2− 49

10. 8 − 3𝑥

8 + 3𝑥 = 9𝑥2− 64

A quadratic equation is an
equation of degree 2. Its
highest exponent is 2. It
can be written in the form
𝒂𝒙𝟐+ 𝒃𝒙 + 𝒄 = 𝟎 , wherein
𝒙 is the unknown, 𝒂, 𝒃, and

𝒄 are real numbers and

𝒂 ≠ 𝟎.

Why do you think a
must not be equal
to zero in equation
𝑎𝑥2+ 𝑏𝑥 + 𝑐 = 0?
Because if a = 0, 𝑎𝑥2will

become 02=0 (any number
multiplied by zero is equal to
zero). The equation is not a
quadratic since the degree is

no longer 2.

The equation 𝑎𝑥2+ 𝑏𝑥 + 𝑐 = 0 is

the standard form of a

quadratic equation; a stands
for the number that is the
coefficient of 𝒙𝟐, b for the

coefficient of x, and c for the

constant term.

In the equation

𝑎𝑥2, is the quadratic

term, 𝑏𝑥 is the

linear term, and 𝑐 is

the constant term.
Forms of Quadratic Equation

1.𝑎𝑥2+ 𝑐 = 0
2. 𝑎𝑥2+ 𝑏𝑥 = 0

3. 𝑎𝑥2+ 𝑏𝑥 + 𝑐 = 0

Tell whether each

equation is quadratic

or not quadratic.

a. x2+ 7x + 12 = 0
b. -3x (x + 5)= 0
c. 12 – 4x = 0
d. (x + 7) (x – 7) = 3x
e. 2x+ (x + 4) = (x – 3)+ (x – 3)

Write each equation in
standard form then identify
the values of a, b, and c.

1. 𝟐𝒙𝟐+ 𝟓𝒙 – 𝟑 = 𝟎
2. 𝟑𝒙 – 𝟐𝒙𝟐= 𝟕
3. 𝟐𝒙𝟐− 𝟑𝒙 + 𝟕 =
3.

𝒙 𝟒𝒙 + 𝟔 = 𝟐𝟖

4.

𝟒𝒙𝟐+ 𝟔𝒙 − 𝟐𝟖 = 𝟎

4.

𝟐𝒙 + 𝟓

𝒙 − 𝟏 = −𝟔

5.

𝟐𝒙𝟐+ 𝟑𝒙 − 𝟓 = 𝟎

Identify which of the following
equations are quadratic and
which are not.

1. 3𝑚2+ 8 = 15
2. 12 – 4𝑥 = 0
3. 10– 7𝑡 = 𝑡2
4. ℎ(ℎ2− 6) = 0
5. 3 (𝑥 − 2) = −7
6.

𝑟 − 12= −7

Write each quadratic equation in
standard form, ax2 + bx + c = 0 then
identify the values of a, b, and c.

1. 3𝑥 − 2𝑥2= 7
2.

𝑥 + 3

𝑥 + 4 = 0

3.

2𝑥

𝑥 − 3 = 15

4.

𝑥 − 42+ 8 = 0