Question

What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

f(x) = 1/8(x − 3)^2 + 3
f(x) = −1/8 (x − 3)^2 + 3
f(x) = 1/8 (x − 3)^2 − 3
f(x) = −1/8(x − 3)^2 − 3

Answer 1

They All are moved 3 points right visible from (x-3) , The graph is one point up. It is a parabola means [ a(x-x0)^2 - D/4a ]. This is the formula. D is Discriminate. x0 (BUT NOT - x0) is the x coordinate of focus and (-D/4a) is the Biggest or smallest value of graph. that is y.
if a > 0 then we have smallest value y if a< 0 then we have biggest value y. Logically if The given y is greater than focus y0 coordinate then a can't be smaller than 0. a > 0 for sure. now we have 1 or 3 . so Logically the distance from y=5 should be 1. Sorry for bad answer. Hope that helps you.