Given the directrix of y = −1 and focus of (0, 3), which is the equation of the parabola?
y = one eighthx2 − 1
y = −one eighthx2 + 1
y = one eighthx2 + 1
y = −one eighthx2 − 1

third choice.

step-by-step explanation:

this a parabola is opened up since the directrix is under the focus and the directrix is horizontal.

this means the square part will be on the x:

the vertex is (h,k).

we already determined p was positive because it is faced up.

|p| also gives us the distance between the focus and the vertex or the distance between the vertex and the directrix.

this means 2|p| gives us the distance between the directrix and the focus.

the distance between the directrix y=-1 and the focus   (0,3) is )=4.

so 2|p|=4.

divide both sides by 2:

|p|=2

p=2 or p=-2

p=2 means the parabola is faced up.

p=-2 means the parabola is faced down.

we already determine p is positive so p=2.

  so we have this so far:

now the vertex lays halfway between the directrix y=-1 and the focus (0,3), so the vertex is .

plug in (h,k) as (0,1) to give us:

solve for y.

distribute:

add 8 on both sides:

divide both sides by 8:

simplify both sides:

answer: 414,377,008

step-by-step explanation:

just multiply it

the correct answer would be the third option