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Fun with Math

Fun with Math

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Author: Ethan Smith
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The objective of this lesson is to utilize the Quadratic Formula to solve quadratic equation.

In this lesson, you will learn how to use the Quadratic Formula to solve quadratic equations. The examples used have REAL solution (not imaginary). There is also a video included to help you remember the quadratic formula.

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Tutorial

Solving a Quadratic Equation Using the Quadratic Formula

Introduction

In this lesson, we wish to use the Quadratic Formula to solve quadratic equations. What's so special about the Quadratic Formula? IT ALWAYS WORKS! That's right, regardless of the numbers, this method always works. Let's begin by getting the stuff we need to start solving.

Standard Form of a Quadratic Equation

The standard form of a quadratic equation is a x squared plus b x plus c equals 0. Notice that the equation is equal to zero. This is important. To ue the Quadratic Formula, our equation MUST be equal to zero.

The Quadratic Formula

The quadratic formula looks intimidating at first, but it uses the same letters as standard form. Let's look at what the Quadratic Formula looks like.

x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction

*It is important to note that the b is squared. That means we need to use parenthesis when we calculate the value.

Now, let's look at an example of how to use this wonderful tool to do some algebra.

Example 1

Solving the quadratic equation x squared plus 2 x plus 1 equals 0 using the quadratic formula.

Step 1: Make sure the equation is equal to zero.

This step is done for us! Great!

Step 2: Determine what the values of a, b, and c are in the equation.

Here the value of a is one. Even thought doesn't look like there is a number in front of x squared, there is: one! The value of b is 2, and the value of c is one.

Step 3: Substitute your values from Step 2 into the Quadratic Formula.

x equals fraction numerator negative left parenthesis 2 right parenthesis plus-or-minus square root of left parenthesis 2 right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis 1 right parenthesis end root over denominator 2 left parenthesis 1 right parenthesis end fraction

Notice what I did there? I put ALL of the values in parenthesis. This will help me from making an error in my arithmetic later on in the problem.

Step 4: Simplify

x equals fraction numerator negative 2 plus-or-minus square root of 0 over denominator 2 end fraction, the square root of zero is zero, so that goes away.

x equals fraction numerator negative 2 over denominator 2 end fraction

x equals negative 1

And we're done simplifying!

Step 5: Check your answer.

It is a good habit to always check your answer to make sure that you did your work correctly. We do this by plugging in the value we found (x equals negative 1) back into our original equation.

left parenthesis negative 1 right parenthesis squared plus 2 left parenthesis negative 1 right parenthesis plus 1

1 minus 2 plus 1, since one squared is one and 2 times negative 1 is negative 2

0!

That is what we wanted! And we're done!

Quadratic Formula Song

Some people have a hard time remembering the Quadratic Formula. This little song may help!