Mathematics
Mathematics 9
First Quarter
Chapter 1
Quadratic Equation
Introduction to
Quadratic Equation
Prepared by: Ms. Amanda Jane R. Regua
Let’s Review
Given the polynomial,
answer the following;
1. What is the exponent of the first term?
2
2. What is the highest exponent?
2
3. What is the numerical coefficient of the second term?
-3
4. What is the variable used in the equation?
x
Let’s Review
Given the degree of the following polynomials.
1. x3 + 4x – 2 = 0
Third degree
2. x – 6x2 = 1 0
Second degree
3. 9 – 5x = 0
First degree
4. -2x4 – 3x2 + x – 3 = 0
Fourth degree
Quadratic Equation
• A Quadratic Equation is an equation involving
a polynomial at the second degree. This
means that the highest exponent that a
quadratic equation can have is 2. This can be
written in standard form as
ax2 + bx + c = 0
where a, b, and c are real numbers and a is not
equal to 0, (a ≠ 0 ).
Examples of Quadratic Equations
1.5x2 = 0
2.2x2 – 5x + 11 = 0
2
3.x - 8 = 0
2
4.5x + x = 13
5.3x = 10 + 8x2
Examples of NOT Quadratic Equations
1. 5x + 1 = 0
2. 4x⁻2 + 6x – 10 = 0
3.
+ 4x – 14 = 0
4. 6a3 – 25a + 30 = 0
the exponent is 1
NOT a degree of 2
the exponent is
negative
the variable is in the
denominator.
NOT a degree of 2
since the highest
exponent is 3
Parts of a Quadratic Equation
In Quadratic Equation ax2 + bx + c = 0,
• the ax2 term is called the Quadratic
term.
• the bx term is called the Linear term.
• the c term is called the Constant
term.
Study the table below.
Questions:
1. What is the exponent of the variables in the column Quadratic
2
Term?
2. What is the exponent of the variables in the column Linear
Term?
1
• Note: In quadratic equations ax2 + bx + c = 0,
the value of a should not be equal to zero
(a≠0) . Hence it is NOT a quadratic equation, it
will be a LINEAR Equation.
Example: 4x + 1
 4x = linear term
 1 = is the constant term
Since there is no ax2 or the quadratic term the
value of a is zero.
 Therefore, it is not a quadratic equation but a
Linear equation wherein the highest exponent
is 1 and it is in the form bx + c = 0.
Standard Form of Quadratic Equation
• A Quadratic Equation is written in Standard
Form as ax2 + bx + c = 0
Simplify the equations then write to
standard form
Apply the distributive method
Transfer -1 to the left side
that will become positive 1
We get the Standard form
Simplify the equations then write to
standard form
Apply the FOIL method
Combine similar terms.
Transfer – 20 to the left side
that becomes + 20
Add or Subtract constant terms
We get the Standard form
Simplify the equations then write to
standard form
Apply the FOIL method
Combine similar terms.
Transfer 2b to the left side
that becomes -2b
Combined similar terms
We get the Standard form
Identify the values of a, b, and c.
Quadratic Equations
1.4x2 – x + 5 = 0
2. x2 – 7x – 3 = 0
3. -4x2 + 5x + 7 = 0
4. x2 – 2 = 0
5. 3x2 = 0
a
b
c
4
1
-4
1
3
-1
-7
5
0
0
5
-3
7
-2
0
EXERCISES
A. Direction: Read the following questions and choose the correct answer.
B. Direction: Read each statement and choose the correct answer. Write
TRUE if the statement is correct and FALSE if it is not true.
Identify if it is Quadratic Equation or
Not a Quadratic Equation.
1.
2.
3.
4.
5.
x2 – 4x – 3 = 0
-2x3 + x2 + 1 = 0
6x + 1 = 0
9x2 = 0
(x + 1) (x -2) = 0
Quadratic Equation
Not Quadratic Equation
Not Quadratic Equation
Quadratic Equation
Quadratic Equation
Write in standard form and identify
the values of a, b, and c.
Quadratic Equations
1. 3x2 – 3 = – 2x
2. 8 = – x + 4x2
3. 6x – 7 = 3x2
4. -x2 = - 6
5. 9x2 = 0
Standard Form
a
b
c
Write in standard form and identify
the values of a, b, and c.
Quadratic Equations
Standard Form
a
b
1. 3x2 – 3 = – 2x
3x2 + 2x – 3 = 0
2. 8 = – x + 4x2
- 4x2 + x + 8 = 0 - 4 1
3. – 7 + 6x = 3x2
-3x2 + 6x – 7 =0
c
3 2 -3
8
-3 6 -7
4. -x2 = - 6
-x2 + 6= 0
-1 0
6
5. 9x2 = 0
9x2 = 0
9 0
0
Simplify the equation then write the standard
form and identify the values of a, b, and c.
1. (x + 7) (x – 3) = 7 + x
Standard Form
x2 + 3x – 28 = 0
a=1
b=3
c = -28
Thank you and God bless!
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