Question

help?!?!!Algebra 2!

Answer 1

First we need the focal distance p.

Since the directrix is in the form y = k, we subtract the y coordinates of the focus and the directrix. Then take the absolute value

|-1 - (-1/2)|

|-1+1/2|

|-1/2|

1/2

So that means p = 1/2. This is the distance from the focus to the vertex.

Answer 2

Actually sorry, I forgot to cut that distance in half

Answer 3

cut 1/2 in half to get (1/2)*(1/2) = 1/4

Answer 4

So p = 1/4

Answer 5

This is the distance from the focus to the vertex

This means you start at (2,-1) and go 1/4 unit up to get to (2,-3/4)

The vertex is (2,-3/4)

Answer 6

This means (h,k) = (2,-3/4) ----> h = 2, k = -3/4

Answer 7

Plug p = 1/4, h = 2, k = -3/4 into the formula below and solve for y



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

4(1/4)(y-(-3/4)) = (x-2)^2

1(y+3/4) = (x-2)^2

y+3/4 = (x-2)^2

Now since the directrix is above the focus, this makes the parabola open downward, so we need to stick a -1 on the (x-2)^2 term

y+3/4 = -(x-2)^2

then continue to solve for y

y = -(x-2)^2 - 3/4