Quadratic Equations
A Quadratic equation is a type of equation in which the highest power of the
variable is 2. It is called “quadratic” because the variable is squared.
The standard form of a Quadratic equation is : ax2 + bx + c = 0
Where: a, b, and c are real numbers
a≠0
x is the variable
If a = 0, the equation becomes a linear equation, not a quadratic equation.
Examples of Quadratic Equations
1. x2 + 5x + 6 = 0
2. 2x2 – 3x + 1 = 0
3. x2 – 9 = 0
All of these are quadratic equations because the highest power of x is 2.
Important Parts of a Quadratic Equation
In the equation: ax2 + bx + c = 0
a is the coefficient of x2
b is the coefficient of x
c is the constant term
Example:
For 2x2 + 3x – 5 = 0
a=2
b=3
c = -5
Created by Ash
Quadratic Equations
, Graph of a Quadratic Function
When a quadratic equation is written in the form Y
Y = ax2 + bx + c, its graph forms a curve called a
X
Parabola. The parabola opens upward if a > 0 X’
and downward if a < 0. The point where the parabola
changes the direction is called the vertex, which is the
highest or the lowest point of the graph. Y’
Methods to solve Quadratic Equations
1. Factorization method
In this method, the Quadratic expression is factorized into two binomial
factors. After factorization, the Zero Product Property is used to find the
values of the variable.
2. Completing the Square Method
In this method, the quadratic equation is rewritten as a perfect square. Then
the square root of both sides is taken to find the value of the variable.
3. Quadratic Formula Method
This method uses a formula that works for all quadratic equations, especially
when factorization is difficult.
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Created by Ash
Quadratic Equations
A Quadratic equation is a type of equation in which the highest power of the
variable is 2. It is called “quadratic” because the variable is squared.
The standard form of a Quadratic equation is : ax2 + bx + c = 0
Where: a, b, and c are real numbers
a≠0
x is the variable
If a = 0, the equation becomes a linear equation, not a quadratic equation.
Examples of Quadratic Equations
1. x2 + 5x + 6 = 0
2. 2x2 – 3x + 1 = 0
3. x2 – 9 = 0
All of these are quadratic equations because the highest power of x is 2.
Important Parts of a Quadratic Equation
In the equation: ax2 + bx + c = 0
a is the coefficient of x2
b is the coefficient of x
c is the constant term
Example:
For 2x2 + 3x – 5 = 0
a=2
b=3
c = -5
Created by Ash
Quadratic Equations
, Graph of a Quadratic Function
When a quadratic equation is written in the form Y
Y = ax2 + bx + c, its graph forms a curve called a
X
Parabola. The parabola opens upward if a > 0 X’
and downward if a < 0. The point where the parabola
changes the direction is called the vertex, which is the
highest or the lowest point of the graph. Y’
Methods to solve Quadratic Equations
1. Factorization method
In this method, the Quadratic expression is factorized into two binomial
factors. After factorization, the Zero Product Property is used to find the
values of the variable.
2. Completing the Square Method
In this method, the quadratic equation is rewritten as a perfect square. Then
the square root of both sides is taken to find the value of the variable.
3. Quadratic Formula Method
This method uses a formula that works for all quadratic equations, especially
when factorization is difficult.
−�± �2 −4��
�= 2�
Created by Ash
Quadratic Equations
