Question

Let f(x)=x^2 +2x-15 . Determine the values of x for which a) f(x)=-12

Answer 1

f(x)=x^2 +2x-15

-12=x^2 +2x-15

0 = x^2 +2x-15 +12

0 = x^2 +2x-3

x^2 +2x-3 = 0

I'll let you finish

Answer 2

THe answer says its a x,y coordinate

Answer 3

Solve for x. Once you get the solutions for x, you can find the corresponding values for y.

Answer 4

I am sorry, I am just very confused.

Answer 5

COuld you help me any further or is that all?

Answer 6

I don't get how it fits into a co ordinate

Answer 7

try to solve that quadratic for x (factor or use the quad formula)

Answer 8

would quadratic be easier?

Answer 9

no.

Answer 10

o ohkay thank you

Answer 11

i Haven't factored in forever how would you factor: x^2+2x-3?

Answer 12

what are the factors of -3?

Answer 13

why does that matter

Answer 14

factored form of a quadratic looks like (x +a)(x +b)

Answer 15

Yes I understand that part

Answer 16

notice that a times b is going to have to equal the constant term in your quadratic

Answer 17

your quadratic's constant term is -3

Answer 18

So those two have to equal that?

Answer 19

so if you can find the factors of -3 you'll have a few guesses as to what a and b should be, and you can check to see if your guesses work or not

Answer 20

1, -3

Answer 21

how would i write the part of (x + a) (x+b)

Answer 22

(x+1) (x-3)?

Answer 23

(x +3)(x -1) =?

Answer 24

yes:)

Answer 25

Oh I see and the -3 constant can just disapear?

Answer 26

no, of course not.

Answer 27

expand that factored form and see if it matches the equation you are trying to factor. If it does, you have found the factors of the equation.

Answer 28

if it doesn't then try the factors:
(x -3)(x +1) =?

Answer 29

how would you expand once more?

Answer 30

because the answer is incorrect it should be the opposite signs on the numbers

Answer 31

?

Answer 32

expand like this: (x +3)(x -1) = x(x-1) + 3(x-1)

Answer 33

finish that up and see if it matches the original equation you're trying to factor.

Answer 34

i got 5x-2

Answer 35

that is not the orignal equation

Answer 36

x*x =?
x*(-1) =?
3*x =?
3*(-1) =?

Answer 37

when you get done, add any like terms.

Answer 38

Its 5x -2

Answer 39

try again

Answer 40

oh my god

Answer 41

4x-3?

Answer 42

what is x times x?

Answer 43

2x

Answer 44

x^2

Answer 45

what about the imaginary 1 infront

Answer 46

wait nvm i'm dumb

Answer 47

3*3 = 2*3?
4*4 = 2*4?
5*5 = 2*5?

Answer 48

3*3 = 3^2
4*4 = 4^2
5*5 = 5^2

Answer 49

*= to multiplying?

Answer 50

yes

Answer 51

use * or ( ) for multiplication from now on or you'll get multiplication confused with an 'x'

Answer 52

how is 3*3= 2*3 as you wrote above

Answer 53

3x3 is 9 and 2x3 is 6

Answer 54

it's not. That's what you were saying. x*x isn't 2*x I was showing you how to prove it to yourself by using actual numbers. 3*3 is clearly not 2*3 it's 3^2

Answer 55

okay well anyways back to the question

Answer 56

yep

Answer 57

let me know when you've found

x*x =?
x*(-1) =?
3*x =?
3*(-1) =?

and added the like terms

Answer 58

x^2+2x-3?

Answer 59

yep

Answer 60

it matches the equation you were trying to factor. So therefore you have found the factored form.

Answer 61

(x-3)(x+1) is the factored form of x^2+2x-3
Now we use it to find
(x-3)(x+1) =0

Answer 62

what values of x make that last statement true?

Answer 63

3 and -1?

Answer 64

yes

Answer 65

so those are the two solutions to x^2 +2x-3 = 0

Answer 66

Okay but in my book it says the answers are -3, and 1

Answer 67

thats why i'm wondering

Answer 68

Yeah
we were actually expanding (x+3)(x-1) not (x-3)(x+1)

so (x+3)(x-1) =0
that's the one you need to use to find x

Answer 69

-3 and 1

Answer 70

So what is the distinguishing factor for me to know if i should use -3 and 1 or 3 and -1

Answer 71

just the steps we went over... try expanding (x-3)(x+1) and see what you get.
You won't get x^2 +2x-3

Answer 72

after you do a few you won't often need to go through these steps. It'll just be something you can do in your head by looking at the problem for a minute or two.

Answer 73

so you just knew that it was -3 and 1 without doing none of those steps :/

Answer 74

well, here's a little trick or short cut:
x*x =?
x*(-1) =?
3*x =?
3*(-1) =?
look at that part again... see how there are two terms with x in them? (-x and 3x)
those have to add to give you the 'x' term in your original...

Answer 75

so your two terms a and b in (x+a)(x+b) have to multiply to give you -3
and add to give you 2

Answer 76

I Just did (x+1) (x-3) and the oppostie way with a formula called FOIL (First, outside, inside, last) and both gave me x^2+2x-3

Answer 77

bit of practice and you can do that part pretty quickly in your head, if you can also find the factors of the constant term in your head eg.:
x^2 -6x +9
a*b = 9
a+b =-6
factors of 9 we will use that add to -6 must be -3 and -3
so (x-3)(x-3) is the factored form and the solutions are x= 3,3

Answer 78

But yes I understand now that they must multiply to give you the constant and add to give you the number infront of the x alone

Answer 79

yep:) exactly. and hopefully you also know why it has to work like that now:)

Answer 80

Yes, so it came down to factoring :), and this would have worked with the quadratic formual as well?

Answer 81

of course. lot more work however...

Answer 82

yea

Answer 83

I'm just wondering are you a teacher or just someone well educated on the topic?

Answer 84

I work for a math and physics education company. (no, not Kahn Academy)

Answer 85

Oh I see, and you enjoy to help students?

Answer 86

yep

Answer 87

Okay, well thank you very much again, I appreciate what you're doing keep it up :)

Answer 88

No problem!