OpenStudy (anonymous):

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

3 years ago
OpenStudy (somy):

@Kainui

3 years ago
OpenStudy (anonymous):

@satellite73 @amistre64

3 years ago
OpenStudy (anonymous):

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 \[(y-k)^2=4p(x-h)\]

3 years ago
OpenStudy (anonymous):

i think its vertical

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

i don't understand what P is

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

Sure

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (amistre64):

p is the distance from v to d right?

3 years ago
OpenStudy (amistre64):

which is the same distance from v to f

3 years ago
OpenStudy (anonymous):

so its 1/2

3 years ago
OpenStudy (anonymous):

then i get x^2=2y?

3 years ago
OpenStudy (amistre64):

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

3 years ago
OpenStudy (amistre64):

-x^2 = 2y

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (amistre64):

yep

3 years ago
OpenStudy (amistre64):

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

3 years ago
OpenStudy (anonymous):

so can the equation we got be simplified any more?

3 years ago
OpenStudy (amistre64):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (amistre64):

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

3 years ago
OpenStudy (anonymous):

so i would just find the middle of the 2?

3 years ago
OpenStudy (anonymous):

so would it be -3,4?

3 years ago
OpenStudy (amistre64):

yes, assuming the directrix is y=N maybe?

3 years ago
OpenStudy (anonymous):

what is N?

3 years ago
OpenStudy (amistre64):

the number of x or y that defines the directrix

3 years ago
OpenStudy (amistre64):

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

3 years ago
OpenStudy (amistre64):

well, -4 but still

3 years ago
OpenStudy (anonymous):

x=-4

3 years ago
OpenStudy (anonymous):

|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.

3 years ago