Solving a Quadratic Equation Using a Graph
(KS4, Year 10)
The LessonA 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 GraphSolving a quadratic equation using a graph is easy.
QuestionSolve the quadratic equation shown below using a graph.
Draw the quadratic equation on a pair of axes.
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.
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.
Lesson SlidesSometimes 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. Open the slider in a new tab
3 Cases of Roots on a GraphThere 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.
Interactive WidgetYou can use this interactive widget to create a graph of your quadratic equation. Use the buttons to change the values of the quadratic equation.
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