# How to Solve Quadratic Equations Using the Graphical Method (Mathematics Lesson)

# 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

Step 2

Step 3

x

_{1}= -1

Step 4

x

_{2}= 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 Test

**show**

##### Note

# 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.