Need help on this asap!!

Question

Find the directrix for the parabola

Answer 1

vertex = (2,-1). focus y value + 1 = h+ 1 = distance from vertex to focus = distance from vertex to directrix

a point on the parabola horizontally from the focus has x value = 2h+2+2 = 2h+4 = distance from the vertex to the directrix line y=-h-2

the point on the parabola vertically above the directrix is (2h+4,h) plug that value into the parabola equation to get h+1 = (1/16)(2h+4-2)^2

solve for h

4h^2 -8h -12 = 0

h =3, -1

with h=3, the focus is (2,3) and directrix is y=-5

It's an upward opening parabola, which is fairly "flat" due to the 1/16 coefficient. x intercepts are (6,0) and (-2,0), each 4 units horizontally from the axis of symmetry x=2.

the focus is 4 units above the vertex, 3 to -1, just as the directrix is 4 units below the vertex -1 to -5

Answer 2

y = a(x - h)² + k

y = a(x - 2)² - 1

Directrix

y = k - p

y = -1 - p

p = 1 / 4(1/16)

p = 4

y = -1 - 4