# How to Solve Quadratic Equations Using the Graphical Method

A quadratic equation can be solved by drawing the equation on a graph and seeing where the curve crosses the x-axis:

# A Real Example of How to Solve Quadratic Equations Using the Graphical Method

Question: Solve the quadratic equation below using the graphical method.

Step 1
Draw the quadratic equation on a pair of axes.

Step 2
Identify the x-intercepts; where the curve crosses the x-axis.

Step 3
Read off the x-value of the first x-intercept. This is the first root of the quadratic equation.

x1 = -1

Step 4
Read off the x-value of the second x-intercept. This is the second root of the quadratic equation.

x2 = 3

The solution to the quadratic equation is x = -1 or x = 3.

# A Real Example of How to Solve Quadratic Equations Using the Graphical Method

Sometimes quadratic equations have repeated roots - that is the same number solves the quadratic equation twice..

The slider below shows how to solve a quadratic equation where there are repeated roots.
##### Interactive Widget
Here is an interactive widget to create a quadratic equation.
show

# THE 3 CASES SEEN GRAPHICALLY

There are 3 possible cases for the roots of a quadratic equation.

• 2 real, distinct roots. Occurs when the curve crosses the x-axis in two places.

• 1 repeated root. Occurs when the curve touches the x-axis at one point.

• 2 complex roots. Occurs when the curve does not touch the x-axis at all.