Question

Rico is drafting a parabola on a coordinate plane. He wants the focus to be at (0,4)
(
0
,
4
)
and the directrix to be y=2
𝑦
=
2
. What will be the equation, in standard form, that matches this parabola? Fill in the missing values of the equation.(1 point)
y=
𝑦
=
x2+3

Answer 1

Vertex is halfway between focus (0,4) and directrix y=2, so vertex (0,3). p = 1, so (x−0)^2 = 4p(y−3) → x^2 = 4(y−3). Solving for y gives

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