# Math Help: The Quadratic Formula

08/14/2015

## Algebra Help: Using the Quadratic Formula

Use the quadratic formula to solve single-variable, second order polynomials, where the highest exponent is 2. These are a specific kind of equation called quadratic equations written in the form ax^2+bx+c=0. This article will build upon our previous post on mastering the basics of math by showing how to use the quadratic formula.

### What Is the Quadratic Formula?

In a quadratic equation, ax^2+bx+c=0, we will place the values of the constants (a, b, and c) into the following formula: x= (-b±√(b^2-4ac))/2a The quadratic formula is very easy to use. Just plug in the values of your quadratic equation's constants and solve for x. It may be difficult to memorize, however, which will happen after practice. Let's take a look at some examples.

### Example 1

Solve the quadratic equation 2x^2-4x+2=0 using the quadratic formula.

### Step 1:

First make sure that your equation is quadratic. We see only one variable, x; the highest exponent is 2; and the equation equals 0. Now we can move forward.

### Step 2:

Define our constants and plug them into the formula. a=2, b=-4, and c=2. Using the formula, we have x=(-(-4)±√(-4^2-4(2)(2))/2(2). Simplifying gives us x=(4±√(16-16))/4. Solving results in x=1. If you plug 1 in for x into the equation, you will see that it works. 2(1^2)-4(1)+2=0 gives us 2-4+2=0.

### Graphic Interpretation

In our first example, we only got one answer for x, but notice the ± sign in the quadratic formula. When there is a value other than 0 in the square root, we will obtain two answers for x. This is because quadratic equations are parabolas, and a parabola can cross the y-axis twice.

### No Real Answer

If you get a negative number in the square root, that means there are no real answers for x. Be on the lookout for this possibility if b^2 is smaller than 4ac.

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