Question

Question #7296f

Answer 1

`y = 5`

Explanation:

Given: `-8 (y-3)=(x+4)^2`

We want to write the equation in the vertex form, `y = 1/(4f)(x-h)+k`, because we know that the equation of the directrix is `y = k-f`

Multiply both sides by `-1/8`:

`y-3=-1/8(x+4)^2`

Make the equation fit the form `x-h` by writing `x+4` as `x - (-4)`:

`y-3=-1/8(x- (-4))^2`

Add 3 to both sides of the equation.

`y=-1/8(x- (-4))^2+3`

Now, that we have the equation in vertex form, we can observe that `k = 3` and we can compute the value of f:

`1/(4f) = -1/8`

`4f=-8`

`f = -2`

Use the pattern, `y = k-f`, to write the equation of the directrix:

`y = 3 - (-2)`

`y = 3+2`

`y = 5`