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 x2 − 3x + 2.

Plot y = x2 − 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.

Slider

Sometimes quadratic equations have repeated roots: the same value of x solves the quadratic equation twice.

The slider below shows another real example of how to solve a quadratic equation using a graph.

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See Also

What is a graph? What is the x-axis? What is a x-coordinate?