Question

please please please help,What is the equation of the parabola, in vertex form, with vertex at (-2,-4) and directrix x = -6?

Answer 1

we can do this, just give me a second to make sure my answer is correct

Answer 2

ok thank you

Answer 3

good thing i checked, it wasn't
let me start again

Answer 4

alright no problem thank you for helping

Answer 5

ok i made mistake in writing it but now i have it

Answer 6

first of all since \(x=-6\) is a vertical line, and the vertex is to the right of the directrix you know it looks like this

Answer 7

yes

Answer 8

crappy picture but you get the idea
we need to know that because that tells you that the \(y\) term is squared

Answer 9

therefore the standard form of this will be
\[(y+k)^2=4p(x-h)\] where the vertex is \((h,k)\) so we know right away that it is
\[(y+4)^2=4p(x+2)\]
now all we need is \(p\)

Answer 10

typo there, standard form is
\[(y-k)^2=4p(x-h)\]

Answer 11

i really appreciate the help and explanation i suck at this

Answer 12

is it okay so far?
vertex is \((-2,-4)\) so we know it must be \[(y+4)^2=4p(x+2)\]

Answer 13

now to find \(p\) the vertex is \((-2,-4)\) and the directix is \(x=-6\)
the distance between \(-6\) and \(-2\) is \(4\) i.e. the directrix is 4 units to the left of the vertex
this tell you \(p=4\) and so \(4p=16\)

Answer 14

therefore your parabola is
\[(y+4)^2=16(x+2)\]

Answer 15

that helped so much thank you :)

Answer 16

you can check (like i did) that this is correct here
http://www.wolframalpha.com/input/?i=parabola+%28y%2B4%29^2%3D16%28x%2B2%29

Answer 17

yw