# How to Solve a Quadratic Equation Using a Graph

## Solving a Quadratic Equation Using a Graph

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 ^{2} − 3x + 2**.

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

We can see that **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**.