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How to Solve Quadratic Equations Using the Graphical Method (Mathematics Lesson)

How to Solve Quadratic Equations Using the Graphical Method

A quadratic equation can be solved by drawing the equation on a graph and seeing where the curve crosses the x-axis:



A Real Example of How to Solve Quadratic Equations Using the Graphical Method

Question: Solve the quadratic equation below using the graphical method.



Step 1
Draw the quadratic equation on a pair of axes.



Step 2
Identify the x-intercepts; where the curve crosses the x-axis.



Step 3
Read off the x-value of the first x-intercept. This is the first root of the quadratic equation.



x1 = -1

Step 4
Read off the x-value of the second x-intercept. This is the second root of the quadratic equation.



x2 = 3

The solution to the quadratic equation is x = -1 or x = 3.

A Real Example of How to Solve Quadratic Equations Using the Graphical Method

Sometimes quadratic equations have repeated roots - that is the same number solves the quadratic equation twice..

The slider below shows how to solve a quadratic equation where there are repeated roots.
Interactive Widget
Here is an interactive widget to create a quadratic equation.
Interactive Test
  show
 
Note

THE 3 CASES SEEN GRAPHICALLY

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.