Question

Quadratic stuff giving me chest pains ._.

Answer 1

y = −3x2 − 12x − 14

y = 3x2 + 12x − 14

y = −3x2 + 12x − 14

y = 3x2 − 12x − 14


Please explain, I don't just want an answer

Answer 2

what is the vertex of this parabola

Answer 3

I don't know, you mean plugging in the number so a= 3x & b=12x.... and putting it into formula or something? o.o

Answer 4

no at this point I just want to know the point that's at the peak of the parabola

Answer 5

think of it as at the very top of the mountain

Answer 6

-2,-2?

Answer 7

in general, a parabola is in vertex form if you see it written like this

y = a(x-h)^2 + k

where

a = deals with how stretched/compressed the graph is
h = x coordinate of vertex
k = y coordinate of vertex

Answer 8

so (h,k) is the vertex

since (-2,-2) is the vertex in this specific case, we know that

(h,k) = (-2,-2)

which means

h = -2 and k = -2

Answer 9

from here, you plug these two values into y = a(x-h)^2 + k to get...


y = a(x - h)^2 + k


y = a(x - (-2))^2 + (-2)


y = a(x + 2))^2 - 2


with me so far?

Answer 10

Yes :)

Answer 11

y= ax + 2a ^2 - 2

Answer 12

now let's use another point on the parabola

notice how the point (-1,-5) lies on the parabola

this means we also know that

x = -1 and y = -5

Answer 13

plug those values in, then solve for 'a', to get

y = a(x + 2)^2 - 2

-5 = a(-1 + 2)^2 - 2

-5 = a(1)^2 - 2

-5 = a(1) - 2

-5 = a - 2

-5 + 2 = a

-3 = a

a = -3

Answer 14

So,

y = a(x + 2)^2 - 2

turns into

y = -3(x + 2)^2 - 2

which is the equation of the parabola in vertex form

Answer 15

what you do from here is expand, distribute, combine like terms and simplify


y = -3(x + 2)^2 - 2


y = -3(x + 2)(x + 2) - 2


y = -3(x(x + 2)+2(x + 2)) - 2


y = -3(x^2 + 2x + 2x + 4) - 2


y = -3(x^2 + 4x + 4) - 2


y = -3x^2 - 12x - 12 - 2


y = -3x^2 - 12x - 14

Answer 16

okay...

Answer 17

it's probably a lot to take in, so just practice practice practice and it'll click better hopefully

Answer 18

I think I get it but when you spit the equation, doing FOIL it kind of threw me off

Answer 19

well that's what FOIL is

you multiply each piece of each binomial with each other

but you're better off breaking it up like I did because you can't use FOIL for something like (a+b)(c+d+e)

but you can use the trick I used to break that up

Answer 20

so it's best to keep in mind that

(a+b)(c+d) = a(c+d) + b(c+d)

Answer 21

thanks :)

Answer 22

you're welcome