The Quadratic Formula - One x-intercept

01
of 06

The Quadratic Formula - One x-intercept

An x-intercept is the point where a parabola crosses the x-axis. This point is also known as a zero, root, or solution. Some quadratic functions cross the x-axis twice. Some quadratic functions never cross the x-axis. This tutorial focuses on the parabola that crosses the x-axis once -- the quadratic function with only 1 solution. 

Four Different Methods for Finding the x-intercept of a Quadratic Function

  • Graphing
  • Factoring
  • Completing the square
  • Quadratic formula

This article focuses on the method that will help you find the x-intercept of any quadratic function - the quadratic formula.

02
of 06

The Quadratic Formula

The quadratic formula is a master class in applying the order of operations. The multistep process may seem tedious, but it is the most consistent method of finding the x-intercepts.

Exercise

Use the quadratic formula to find any x-intercepts of the function y = x2 + 10x + 25.

03
of 06

Step 1: Identify a, b, c

When working with the quadratic formula, remember this form of quadratic function:

y = ax2 + bx + c

Now, find a, b, and c in the function y = x2 + 10x + 25.

y = 1x2 + 10x + 25

  • a = 1
  • b = 10
  • c = 25
04
of 06

Step 2: Plug in the Values for a, b, and c

05
of 06

Step 3: Simplify

Use the order of operations to find any values of x.

06
of 06

Step 4: Check the Solution

The x-intercept for the function y = x2 + 10x + 25 is (-5,0).

Verify that the answer is correct.

Test (-5,0).

  • y = x2 + 10x + 25
  • 0 = (-5)2 + 10(-5) + 25
  • 0 = 25 + -50 + 25
  • 0 = 0