What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5? f(x) = one eighth (x − 3)2 + 3 f(x) = −one eighth (x − 3)2 + 3 f(x) = one eighth (x − 3)2 − 3 f(x) = −one eighth (x − 3)2 − 3

Step-by-step explanation:

We want to find the equation of the parabola with a focus of and directrix .

Considering the directrix, the quadratic graph must open downwards.

The equation of this parabola is given by the formula,

, where is the vertex of the parabola.

The axis of this parabola meets the directrix at .

Since the vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix,

and .

The equation of the parabola now becomes,

.

Also is the distance between the vertex and the directrix.

This implies that .

Since the parabola turns downwards,

.

Our equation now becomes,

.

.

We make y the subject to get,

.

This is the same as

.