Answer:
The required quadratic function is \(y=-\frac{1}{12}(x-3)^2-1\).
Step-by-step explanation:
The standard form of the parabola is
\((x-h)^2=4p(y-k)\)
Where the focus is (h, k + p) and the directrix is y = k - p.
The directrix of y = 2 and a focus of (3, −4).
\((h,k+p)=(3,-4)\)
On comparing both sides we get
\(h=3\)
\(k+p=-4\) ...... (1)
\(y=k-p\)
\(k-p=2\) ...... (2)
Add equation (1) and (2).
\(2k=-2\)
\(k=-1\)
Substitute k=-1 in equation (1).
\((-1)+p=-4\)
\(p=-3\)
Therefore the equation of parabola is
\((x-3)^2=4(-3)(y-(-1))\)
\((x-3)^2=-12(y+1)\)
It can be rewritten as
\(y=-\frac{1}{12}(x-3)^2-1\)
Therefore the required quadratic function is \(y=-\frac{1}{12}(x-3)^2-1\).
