Question

Find the zeroes of the function algebraically

f(x)=x^2+2x-8

Please show step by step!

Answer 1

We have roots (places where the function crosses the x-axis) when f(x)=0.

That will be our first step, let f(x)=0.\[\large 0=x^2+2x-8\]

Answer 2

Are you comfortable with factoring?
This quadratic can be factored quite nicely, it takes a little bit of practice to recognize the right numbers though. :D

Answer 3

factoring? I'm not quite sure what you mean.. It sounds familiar. Can you give me an example?

Answer 4

Oh, they used the word "zeroes", im sorry i misread that.
Zeroes and roots are the same thing.

Answer 5

Sure :)

Answer 6

\[\large 0=x^2+5x+6\]
The idea is, we want to be able to break this down into 2 factors of the form:\[\large 0=(x \pm a)(x \pm b)\]

You want FACTORS of the 6, that ADD to give you 5.
Hmm, So we can get 6 by multiplying 1 and 6.
But 1 and 6 add to 7, hmm that's no good.

How about 3 times 2?
Hmm, 3 and 2 add to make 5! Ooo I think that will work.
Let's set it up,\[\large 0=(x+3)(x+2)\]
If you wanted to verify, you could multiply these out just to check. Remember how to FOIL things? :)

Answer 7

Oh! I remember this! But, I don't know what FOIL is

Answer 8

It's an acronym telling you how to multiply 2 binomials together, (But I can't for the life of me remember what it stands for, lol).

Answer 9

So what you would do for my problem is find what adds to 2 and multiplies to -8
x^2+2x−8
Sooo 4 and -2?

Answer 10

And the equations would be (X+4) (X-2)

Answer 11

right?

Answer 12

Yesss very good \:D/

Answer 13

So the zeroes if the function would be -4 and 2?

Answer 14

Yes good, x=-4, x=2! :)

Answer 15

Sweet! Thanks!