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Solving a Quadratic Equation Using a Graph
(KS4, Year 10)
The Lesson
A quadratic equation can be solved by drawing the equation on a graph and seeing where the curve crosses the xaxis. 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 xaxis.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.StepbyStep:
1
Draw the quadratic equation on a pair of axes.
2
Find the xcoordinate of the first point where the curve crosses the xaxis.
The curve crosses the xaxis at x = −1, which is a solution to the quadratic equation.
3
Find the xcoordinate of the second point where the curve crosses the xaxis.
The curve crosses the xaxis 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 xaxis in two places.

1 repeated root. Occurs when the curve touches the xaxis at one point.
 2 complex roots. Occurs when the curve does not touch the xaxis at all.
Interactive Widget
You can use this interactive widget to create a graph of your quadratic equation. Use the buttons to change the values of the quadratic equation. Do you disagree with something on this page?
 Did you spot a typo?