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 :

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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: