FOIL
FOIL is an operation done to two binomials to find a quadratic equation so that one can graph a parabola.
Let's start with the basics, what's a binomial? It's an equation with two parts that are either added or subtracted. In the case of FOIL, every binomial is constructed so that one of its two parts is an unknown variable (usually x.) Since it’s so hard to explain it in words, let me show you what I mean.
It is important to know, though, that before you FOIL the two binomials to find your quadratic equation, you can set them to zero and solve them separately to find which points on the x-axis your parabola will cross.
For information on what a parabola is and/or how and why it would cross the x-axis, click here. If you don’t know what I mean when I say x-axis, click here.
So, why the heck do I keep on talking about the shiny silver stuff you wrap left-over pizza in? What does old pizza have to do with math? Well, FOIL is actually an acronym that stands for First, Outside, Inside, Last or First, Outer, Inner, Last.
When you have to multiply two binomials together to get a quadratic equation, you start with something that looks like this:
(ax + b) (cx + d)
Of course, numbers will be in place of all the letters besides x. For now, we'll use our own numbers so the letters don't get confusing:
(8x + 3) (2x +4)
As I said before, if you're going to have to find the places that the parabola your equation will graph touches the x-axis, you might as well set this equation to zero and solve for x. This will give you a head start and to make it so you don't have to use the dreaded quadratic formula to find these points.
Now that we know where our parabola crosses the x-axis, we can go on to get our quadratic equation.
First refers to what comes first in each set of parenthesis. After these two variables are found, they are multiplied together to get the first part of your quadratic equation.
(8x + 3) (2x + 4)
8x * 2x = 16x2
Inside/Inner refers to the two variables that are in the inside of the equation (they are sandwiched in by 8x and 4.) These are multiplied together to get another part of your quadratic equation.
(8x + 3) (2x +4)
3* 2x = 6x
Outside/Outer refers to the very first and the very last variables of the equation—the ones that are placed on the very outside of the equation. These are multiplied together to get yet another part of your much anticipated quadratic equation.
(8x + 3) (2x + 4)
8x * 4 = 32x
Last refers to what comes last in each set of parenthesis. These are multiplied together to get the last part of your equation.
(8x + 3) (2x + 4)
3 * 4 = 12
Now, you add all of the separate parts together:
16x2 + 6x + 32x + 12
16x2 + 38x +12
And thus we have our quadratic equation.
"Ok, but now that I have the equation, what am I supposed to do with it? How do I get from that to a parabola?" you're asking. All those questions can be answered by reading our quadratic equation help file.
As a suggestion, you may find it helpful to draw a line connecting each two variables you multiply in the FOIL process. This way you can keep track of what you've already taken care of and you can make fun pictures (who said math couldn't be fun?)
What kind of picture you make all depends on which variables you connect with lines curving upwards or lines curving downwards. Below are a couple I've made, but I'm sure there are more.
To do a FOIL that looks like a fish, curve your lines as follows (with the F and O steps having lines curving upward and the I and L steps curving down):
Related Websites: http://www.freemathhelp.com/using-foil.html
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