Answer: [tex]y=\frac{x^{2}}{4}-x+5[/tex]
Step-by-step explanation:
As the vertex is equidistant from the focus and the directrix, the vertex is (2,4).
This means the equation of the parabola is of the form:
[tex](x-2)^2 = 4p(y-4)[/tex]
The directrix is y = 3, which is the same as y = k - p = y = 4-p, so, so p=1.
So, the equation is:
[tex](x-2)^2 = 4(y-4)\\\\x^2 -4x+4=4(y-4)\\\\ \frac{x^{2}}{4}-x+1=y-4\\\\\boxed{y=\frac{x^{2}}{4}-x+5}[/tex]
