### 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.

### 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* = *x*^{2} + 10*x* + 25.

### Step 1: Identify a, b, c

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

y=ax^{2}++bxc

Now, find *a*, *b*, and *c* in the function *y* = *x*^{2} + 10*x* + 25.

y=1x^{2}+10x+25

- a = 1
- b = 10
- c = 25

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

### Step 3: Simplify

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

### Step 4: Check the Solution

The *x*-intercept for the function* y* = *x*^{2} + 10*x* + 25 is (-5,0).

Verify that the answer is correct.

Test (**-5**,**0**).

*y*=*x*^{2}+ 10*x*+ 25**0**= (**-5**)^{2}+ 10(**-5**) + 25- 0 = 25 + -50 + 25
- 0 = 0