What is the equation of a parabola if

Question

What is the equation of a parabola if

The vertex is ( 1, 7) and the directrix is located at y = 3?

Answer 1

the vertex is equidistant or half way between the focus and the directrix. It has same x value as the vertex, and y value (7-3)+7 = 11. Focus is the point (1,11)

It's an upward opening parabola of general form y = a(x-k)^2 + h where (k,h) is the vertex (1,7)

y = a(x-1)^2 + 7, find another point on the parabola and plug it in to calculate a, the coeffiicent.

try a point horizontally to the right from the focus. It will have a y coordinate = 11. the x coordinate will be the same distance from (1,11) as to y=3. That's equal to 8. 1 to 9 has distance 8. that point on the parabola is (9,11) plug x=9, y = 11 into y =a(x-1) +7 and solve for a.

11= a(9-8)^2 + 7

4 =a

y=4(x-1)^2 + 7

Answer 2

Directrix y = -p, so p here equals -3.

Equation of parabola is (x-h)^2 = 4p(y-k) where h,k is the vertex (1,7)

so substituting h, k and p, the equation is (x-1)^2 = -12(y-7)