The Quadratic Formula - One x-intercept

By
Jennifer Ledwith
Jennifer Ledwith
Math Expert
  • B.B.A., Finance and Economics, University of Oklahoma
Jennifer Ledwith is the owner of tutoring and test-preparation company Scholar Ready, LLC and a professional writer, covering math-related topics.
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Updated on November 05, 2019

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. 

There are four different methods for finding the x-intercept of a Quadratic Function:

  • Graphing
  • Factoring
  • Completing the square
  • Quadratic formula

This tutorial focuses on the parabola that crosses the x-axis once—the quadratic function with only one solution. 

01
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The Quadratic Formula

The quadratic formula is a master class in applying the order of operations. The multi-step 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.

02
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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
03
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Step 2: Plug in the Values for a, b, and c

04
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Step 3: Simplify

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

05
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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
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Ledwith, Jennifer. "The Quadratic Formula - One x-intercept." ThoughtCo, Apr. 5, 2023, thoughtco.com/quadratic-formula-one-x-intercept-2311834. Ledwith, Jennifer. (2023, April 5). The Quadratic Formula - One x-intercept. Retrieved from https://www.thoughtco.com/quadratic-formula-one-x-intercept-2311834 Ledwith, Jennifer. "The Quadratic Formula - One x-intercept." ThoughtCo. https://www.thoughtco.com/quadratic-formula-one-x-intercept-2311834 (accessed April 8, 2025).