Answer:
![f(x)=-\frac{1}{8}(x-3)^2+3](https://tex.z-dn.net/?f=f%28x%29%3D-%5Cfrac%7B1%7D%7B8%7D%28x-3%29%5E2%2B3)
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.
![|p|=2](https://tex.z-dn.net/?f=%7Cp%7C%3D2)
This implies that
.
Since the parabola turns downwards,
.
Our equation now becomes,
.
.
We make y the subject to get,
.
This is the same as
.