write the equation of a parabola given that the vertex is 0,0 and the focus is 0,-1/2

Question

somy · Answer

@Kainui

anonymous · Answer

@satellite73  @amistre64

anonymous · Answer

Well start off by sketching a picture, the vertex is the "centre," and the focus is a fixed point on the interior of a parabola.

Graphing will help you as it will tell you if it's vertical or horizontal, the formulas respectively.

Vertical
$$(x-h)^2=4p(y-k)$$

Horizontal
$$(y-k)^2=4p(x-h)$$

anonymous · Answer

i think its vertical

anonymous · Answer

vertex (h,k) and p = distance and direction from vertex to focus, distance and opposite direction from vertex to directrix.

anonymous · Answer

i don't understand what P is

anonymous · Answer

Cool, if you want further help from me you'll need to tell me more, "i think" is not useful.

anonymous · Answer

ok... so if it was vertical, my equation would be (x-0)^2=4p(y-0)

anonymous · Answer

Sure

anonymous · Answer

so how do i determine what p is? is in -1/2 or 1?

amistre64 · Answer

p is the distance from v to d right?

amistre64 · Answer

which is the same distance from v to f

anonymous · Answer

so its 1/2

anonymous · Answer

then i get x^2=2y?

amistre64 · Answer

good, and our f is in the direction of the opening, so it opens down

amistre64 · Answer

-x^2 = 2y

anonymous · Answer

why is x negative? because the graph is opening downwards?

amistre64 · Answer

yep

amistre64 · Answer

we have a focus under our vertex,  we open towards the focus

anonymous · Answer

so can the equation we got be simplified any more?

amistre64 · Answer

sure it can ... y = ___ x^2

anonymous · Answer

what would i do if i wasnt given the vertex? like focus 4,0 and directrix -4

amistre64 · Answer

focus and directrix are extremes, with the vertex in the middle

anonymous · Answer

so i would just find the middle of the 2?

anonymous · Answer

so would it be -3,4?

amistre64 · Answer

yes,  assuming the directrix is y=N maybe?

anonymous · Answer

what is N?

amistre64 · Answer

the number of x or y that defines the directrix

amistre64 · Answer

a directrix of 4 is not enough information

is it a line thru y=4  or thru x=4?

amistre64 · Answer

well, -4  but still

anonymous · Answer

x=-4

anonymous · Answer

|dw:1412636260222:dw| Drew this out just to show what goes on parabolas as such and what it really means, I hope that helps you visually.