# 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 zeroroot, 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

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

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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.

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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
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## Step 3: Simplify

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

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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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