Solving Quadratic Equations by Factoring 2

Special Report: One of the last Twinkies has been stolen, and it can only be recovered by factoring a quadratic equation. There’s no hurry, though. Those things last forever.

LanguageEnglish Language
Quadratic EquationsQuadratic Equations

Transcript

00:28

However, he also seems really into algebra. Which isÉ kinda creepy.

00:32

You decide to pursue this angle and see where it goes.

00:35

The clown tells you his smile can be modeled by the equation y equals x squared plus 6x

00:42

minus 16.

00:43

How wide is the clownÕs smile? This looks like a quadratic equation.

00:49

Let's take a look at the equation on a graph. To find the width of the clown's smile in

00:54

inches, we can calculate the distance between the x intercepts or roots of the parabola.

01:01

The x intercepts are where the parabola crosses the x axis, which means y equals 0. So let's

01:08

set y to 0 in our equation. y equals x squared plus 6x minus 16, which

01:15

equals zero.

01:18

To find the x values where y equals 0, we can factor the right side into the form "the

01:23

quantity x plus p times the quantity x plus q."

01:28

We can use FOIL to multiply this out. FOIL stands for First, Outer, Inner, then Last.

01:37

So X times X is X-squared, plusÉ

01:40

X times Q is "Q-X", plusÉ

01:43

P times x is "P-X", plusÉ

01:47

P times Q is "PQ".

01:49

Since "PX" and "QX" are like terms, we can add them together to make the quantity P plus

02:00

Q times X.

02:02

Let's look at our original equation to compare.

02:05

We can see that P plus Q equals 6 and P times Q equals negative 16.

02:12

So first, let's find two numbers that multiply together to give negative 16.

02:16

HereÕs a chart of all the factors of negative 16É

02:19

1, negative 16É negative 1, 16É

02:21

2, negative 8É negative 2, 8É

02:23

4 and negative 4.

02:25

We're looking for a "P plus Q" value of 6, which only works for 8 and negative 2.

02:33

That means X squared plus 6X minus 16 can be factored to:

02:37

x + 8É timesÉ x Ð 2 For the equation to equal zero, either X plus

02:43

8 or X minus 2 must equal zero.

02:47

Which means x = -8 and x = 2 So our parabola goes through the x-axis at

02:54

points "negative 8, zero" and "2, zero".

02:59

How does this relate to the clown's smile?

03:01

Well, the width of his smile is the distance between those two points, which is 2 minus

03:06

negative 8É or 10 inches. OkayÉ you decide this clown is definitely

03:10

creepy enough for your little brother.

03:11

However, your plan backfires. Instead of turning him off clowns even moreÉ

03:16

Éyour prank turns him ONTO algebra.

03:19

Great. And he was already the good-looking one.