Question

I WILL MEDAL AND FAN
Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = −one half.

f(x) = −(x + 2)2 − three fourths
f(x) = (x + 2)2 + three fourths
f(x) = −(x − 2)2 + three fourths
f(x) = −(x − 2)2 − three fourths

Answer 1

@Afro @563blackghost @CallMeKiki

Answer 2

@mathstudent55 @ShadowLegendX

Answer 3

ok

Answer 4

sry I don't know

Answer 5

From this we know that p = 1/4 (distance from vertex to directrix)
We know that parabola is negative and opens down
vertex = (2,-3/4)

Equation:
\[y =- \frac{1}{4p}(x-h) + k\]
plugging in values you get:
\[y = -(x-2) - \frac{3}{4}\]