Explanation:
Vertex form of the parabola is
f(x) = a ( x+4)^2 +5 sub in the given point (3,-7) to calculate a = -12/49
-12/49 ( x+4)^2 + 5 expand this to get the quadratic form
-12/49( x^2 + 8x + 16) + 5 simplify it a bit
f(x) = -12/49 x^2 - 96/49 x + 1 4/49