Find the equation of a qudratic function whose graph satisfi

Find the equation of a qudratic function whose graph satisfied the given conditions.

Vertex:(-4,12) y intercept:4

Vertex form of quadratic function: y = a( x -h)^ +k

where (h,k) is vertex ; y intercept =4 ---> ( 0, 4)

Plugging the values in std equation given above.

y = a( x+4)^2 + 12 . Now plug ( 0, 4) to find a

4 = a(0+4)^2 +12 -----> -8 = a*16 -----> a = -1/2

y = - (x+4)^2/2 +12

= {- ( x^2 +16 +8x) + 24 }/2

= (-x^2 -8x -16 -24)/2

= ( -x^2 -8x -40)/2