I'll give you brainliest!

what is the equation of the quadratic graph with a focus of (−4, seventeen eighths) and a directrix of y = fifteen eighths?
a. f(x) = −2x2 + 16x − 24
b. f(x) = −2x2 + 15x − 2
c. f(x) = 2x2 + 12x − 10
d. f(x) = 2x2 + 16x + 34

*and could you explain how to find the *

(x - a)^2 + (y - b)^2 = (y - d)^2 

x^2 - 2ax + a^2 + y^2 - 2by + b^2 = y^2 - 2dy + d^2 

Subtract y^2 from both sides... 

x^2 - 2ax + a^2 - 2by + b^2 = -2dy + d^2 

Now I would just substitute in the the values (a = -4, b = 17/8, d = 15/8)... 

x^2 - 2(-4)x + (-4)^2 - 2(17/8)y + (17/8)^2 = -2(15/8)y + (15/8)^2 

Simplify... 

x^2 + 8x + 16 - (17/4)y + 289/64 = -(15/4)y + 225/64 

Add (17/4)y to both sides... 

x^2 + 8x + 16 + 289/64 = (2/4)y + 225/64 

x^2 + 8x + 16 + 289/64 = (1/2)y + 225/64 

Subtract 225/64 from both sides... 

x^2 + 8x + 16 + 1 = (1/2)y 

x^2 + 8x + 17 = (1/2)y 

Multiply both sides by 2... 

2x^2 + 16x + 34 = y 

...which is equal to equation D.

Idk idk idk idk idk idk idk idk