Question

Parabola equation given somethings

Answer 1

pooja how can i send u a message

Answer 2

Is the focus 0, 22?

Answer 3

Actually since one ordered pair is 14, -22

(14)^2 = a*-22 ?

Answer 4

If you're a human calculator how don't you know this already?

Answer 5

I am broken @OpiGeode

Answer 6

Awww :(

Answer 7

Vertex is (0,0) yes?
and a = 14...

Answer 8

I'm basing this off the assumption that this is an oval shape

Answer 9

...If not then your question broke me too

Answer 10

That's not what he's saying, lol.

Answer 11

you can use the "vertex" form of the equation for a parbola
\[ y = a (x- h)^2 + k \]
where (h,k) is the location of the vertex. Here, the vertex is at (0,0).
so
\[ y = a(x-0)^2 + 0 \\ y = a x^2 \]
to find a, we notice one point on the parabola is at (14, -22)
(14 over (i.e. 1/2 of 28 ), and 22 down from the x-axis )
we get
-22 = a (14)^2
a = -11/98
and
\[ y = - \frac{11}{98} x^2 \]
if you need to find the focus, use
\[ y = \frac{1}{4f} x^2 \]
where f is the distance from the vertex to the focus (in the y direction)
in other words,
\[ \frac{1}{4f} = - \frac{11}{98} \\ 4f = - \frac{98}{11} \\ f= - \frac{49}{22} \]
the focus has the same x value as the vertex, so the focus is at
(0, -49/22)