Question

find the zeros of f(x)= x^2-4x-12

Answer 1

to get zeros of f(x), equate f(x) =0
so can you solve this quadratic ,

x^2-4x-12=0 ??

Answer 2

so i would add -12to zero

Answer 3

then dived by -4?

Answer 4

no, find the factors of -12 that add to -4, the larger is negative and the smaller is positive.

Answer 5

2 numbers whose sum is -4 and product is -12 are.... ?

Answer 6

-6 and 2

Answer 7

correct! so
write -4x as -6x+2x
x^2-6x+2x -12 =0
factor out x from 1st 2 terms and +2 from last 2 terms, what u gt ?

Answer 8

This is a quadratic. You cannot solve a quadratic by simple manipulation (adding to both sides, multiplying, etc)
Instead, you have a few options:
Factoring
Quadratic formula
Completing the square

Answer 9

we are doing factoring method

Answer 10

You'll probably end up learning all of those methods in your class. Which have you studied so far? I would imagine factoring is how your teacher expects you to be doing quadratics so far. Factoring is much simpler to do, but it doesn't always work the way the other two methods always work. Sometimes the quadratic will be unfactorable.

Answer 11

i sorta remember the 6x + 2x part bur not really. i don't understand how to factor it beyond that

Answer 12

ok, take \(\large x^2-6x\) part
it can be written as \(\large x \times x-6\times x=x \times (x-6)\)
got this ? this is factoring x out from 1st 2 terms ...

Answer 13

nowcan u fatcor +2 from +2x-12 ?

Answer 14

10-x?

Answer 15

10? where does 10 come from ?

Answer 16

i don't know? nevermind?

Answer 17

okk..
\(\large 2x-12 = 2\times x-2\times 6 = 2\times (x-6)\)
its just opposite of distributing...u getting this ?

Answer 18

yeah i see what you are saying

Answer 19

Okay, so think of factoring this way:
You're setting up two parenthesis, and then you are trying to fill in those parenthesis so that when you multiply them together, you would get what you started with. Let me show you an example.

\(\Large x^2 + 7x + 10\)
\(\Large(\text{_ }\pm\text{ _})(\text{_ }\pm\text{ _})\)

Answer 20

Now, think about how those parenthesis would get multiplied. Have you practiced FOIL?

Answer 21

good, so we are here now
\(x(x-6)+2(x-6)\)
by exactly same logic, factor out x-6, try ?

Answer 22

yes when i was in algerbra 2 two years ago

Answer 23

Haha okay so do you remember FOILing? Firsts, then Outer and Inner, and then Last.

Answer 24

yes

Answer 25

Okay, so the Firsts part of the multiplying will give you the \(x^2\) part, so in the firsts place of the parenthesis, we put something that will multiply to be \(x^2\).

Answer 26

\((\text{x }\pm\text{ _})(\text{x }\pm\text{ _})\)

Answer 27

Does that make sense?

Answer 28

no? sorry

Answer 29

Being good at factoring is really all about understanding FOIL well, so as much work as it might seem, you should go back and make sure you're good at that. Maybe I need to reexplain it to you.

Answer 30

oh wait, zeros are -2 and +6

Answer 31

Why do you say that? How did you get those numbers?

Answer 32

i factored
(x+2)(x-6)

Answer 33

Okay, cool. You factored correctly =)
To check that it's factored correctly, you would foil that.
\((x+2)(x-6)\)
Firsts gives you x*x = \(x^2\)
Outer gives you x*-6 = -6x
Inner gives you 2*x = 2x
Lasts gives you 2*-6 = -12
So \(x^2 -6x +2x - 12 = x^2 -4x - 12\)
Which means it's factored correctly.

Answer 34

okay awesome thanks

Answer 35

Now factoring doesn't get you the answers immediately, but it gets you super close!

Answer 36

Now that we've factored, the equation we have is
\(\large (x+2)(x-6) = 0\)
think about that equation. I have two things, and I'm multiplying them together, and they equal zero.

Answer 37

What could those things be? How can I have two things, and multiply them together and get 0?

Answer 38

Hello? Thoughts?

Answer 39

Can we finish this question? It pains me to see you get 95% there and then not cross the finish line.

Answer 40

@sarahjones667

Answer 41

okay

Answer 42

Okay, so I multiply two things together, and the result is 0. Can you tell me anything about the two things?

Answer 43

they are 0?

Answer 44

Almost correct. They don't have to both be 0, but at least one of them is.

Answer 45

one is 0 one is 1

Answer 46

Does that make sense?
So if I have
(x+2)(x-6) = 0
What I can decide is, either
(x+2) = 0
or
(x-6) = 0

otherwise, multiplying them together wouldn't give me 0.

Answer 47

Does that much make sense?

Answer 48

yeah it does

Answer 49

Cool, so all we have to do finally is look at those two equations and figure out the x value for either one.
x+2 = 0
what is x?

Answer 50

-2

Answer 51

That's your first zero =)

Answer 52

And your second zero?

Answer 53

+6

Answer 54

Good work =)
So cool. In the future, factor just like that, but remember that you don't get your answer until you figure out what x value would make those factors equal 0.

Answer 55

okay thank ya thank ya

Answer 56

My pleasure =)