The solution of a quadratic equation is the value of x when you set the equation equal to zero
i.e. When you solve the following general equation: 0 = ax² + bx + c
Given a quadratic equation: ax ² + bx + c
The quadratic formula below will solve the equation for zero
The quadratic formula is :
,
Examples of the quadratic formula to solve an equation
Example 1
Quadratic Equation: y = x² + 2x + 1
a = 1
b = 2
c = 1
Using the quadratic formula to solve this equation just substitute a,b, and c into the general formula:
Below is a picture representing the graph of
y = x² + 2x + 1 and its solution
Quadratic Formula Song
A catchy way to remember the quadratic formuls is this song (pop goes the weasal)
Practice Problems
Use the quadratic formula to find the solutions to the following equation:
y = x² − 2x + 1 and its solution
Answer
In this quadratic equation,
y = x² − 2x + 1 and its solution
a =1
b = − 2
c = 1
Use the quadratic formula to find the solutions to the following equation:
y = x² − x − 2 and its solution
Solution(s)
In this quadratic equation,
y = x² − x − 2 and its solution
a =1
b = − 1
c = − 2
Use the quadratic formula to find the solutions to the following equation:
y = x² − 1 and its solution
Answer
In this quadratic equation,
y = x² − 1 and its solution
a = 1
b = 0
c = −1
Calculate the solutions of the the quadratic equation below by using the quadratic formula :
y = x² + 2x − 3 and its solution
Answer
In this quadratic equation,
y = x² + 2x − 3 and its solution
a =1
b = 2
c = −3
Below is a picture of the graph of the quadratic equation and its two solutions
Use the quadratic formula to find the solutions to the following equation:
y = x² + 4x − 5 and its solution
Solution(s)
In this quadratic equation,
y = x² + 4x − 5 and its solution
a =1
b = 4
c = −5
Use the quadratic formula to find the solutions to the following equation:
