Question

write an equation for the parabola
vertex (9,4), focus (9,12)

Answer 1

a = 8 soo and this opens to the .....left

y^2 = 4ax

Answer 2

opps, opens up lol

Answer 3

4ay = x^2

4(8)y = x^2

32y = x^2 then account for the offcenter

Answer 4

32(y-4) = (x-9)^2

y = (1/32)(x-9)^2 +4

Answer 5

Use \[(x-h)^{2} = 4p(y-k) \]
where h is the x coordinate of the focus or vertex (both are the same), k is the y coordinate of the vertex and p is the difference between the two y values

so...
\[(x-9)^{2} = 4(8)(y-4) \]
simplifies to
\[x ^{2} -18x +81 = 32y - 128\]

clean it up to get \[y = 1/32(x ^{2} -18x + 209)\]