## The Lesson

A quadratic equation can be solved by drawing the equation on a graph and seeing where the curve crosses the x-axis. Imagine you wanted to solve the quadratic equation**x**. Plot

^{2}− 3x + 2**y = x**on a graph and read off where the curve crosses the x-axis.We can see that

^{2}− 3x + 2**x = 1**and

**x = 2**solve the quadratic equation.

## How to Solve Quadratic Equations Using a Graph

Solving a quadratic equation using a graph is easy.## Question

Solve the quadratic equation shown below using a graph.## Step-by-Step:

# 1

Draw the quadratic equation on a pair of axes.

# 2

Find the x-coordinate of the first point where the curve crosses the x-axis.
The curve crosses the x-axis at

**x = −1**, which is a solution to the quadratic equation.# 3

Find the x-coordinate of the second point where the curve crosses the x-axis.
The curve crosses the x-axis at

**x = 3**, which is also a solution to the quadratic equation.## Answer:

We have solved the quadratic equation:**x = −1**,

**x = 3**.

## 3 Cases of Roots on a Graph

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.