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.
|Quadratic Equations||Quadratic Equations|
However, he also seems really into algebra. Which isÉ kinda creepy.
You decide to pursue this angle and see where it goes.
The clown tells you his smile can be modeled by the equation y equals x squared plus 6x
How wide is the clownÕs smile? This looks like a quadratic equation.
Let's take a look at the equation on a graph. To find the width of the clown's smile in
inches, we can calculate the distance between the x intercepts or roots of the parabola.
The x intercepts are where the parabola crosses the x axis, which means y equals 0. So let's
set y to 0 in our equation. y equals x squared plus 6x minus 16, which
To find the x values where y equals 0, we can factor the right side into the form "the
quantity x plus p times the quantity x plus q."
We can use FOIL to multiply this out. FOIL stands for First, Outer, Inner, then Last.
So X times X is X-squared, plusÉ
X times Q is "Q-X", plusÉ
P times x is "P-X", plusÉ
P times Q is "PQ".
Since "PX" and "QX" are like terms, we can add them together to make the quantity P plus
Q times X.
Let's look at our original equation to compare.
We can see that P plus Q equals 6 and P times Q equals negative 16.
So first, let's find two numbers that multiply together to give negative 16.
HereÕs a chart of all the factors of negative 16É
1, negative 16É negative 1, 16É
2, negative 8É negative 2, 8É
4 and negative 4.
We're looking for a "P plus Q" value of 6, which only works for 8 and negative 2.
That means X squared plus 6X minus 16 can be factored to:
x + 8É timesÉ x Ð 2 For the equation to equal zero, either X plus
8 or X minus 2 must equal zero.
Which means x = -8 and x = 2 So our parabola goes through the x-axis at
points "negative 8, zero" and "2, zero".
How does this relate to the clown's smile?
Well, the width of his smile is the distance between those two points, which is 2 minus
negative 8É or 10 inches. OkayÉ you decide this clown is definitely
creepy enough for your little brother.
However, your plan backfires. Instead of turning him off clowns even moreÉ
Éyour prank turns him ONTO algebra.
Great. And he was already the good-looking one.