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The  vertex form is

y  = a(x - h) ^2  +  k           where (h, k)  is  the  vertex  and (x,y) is a point on the graph

So

4 = a ( -2-  -3)^2 + 1              subtract 1 from both sides

3 = a ( 1)^2

3  = a (1)

a  = 3

So...the equation is

y = 3 ( x + 3)^2  + 1

The equation of the parabola with vertex (h,k)(h,k) is y=a(−h+x)^2+ky=a(−h+x)^2+k.

Thus, the equation of the parabola is y=a(x+3)^2+1y=a(x+3)^2+1.

To find a, use the fact that the parabola passes through the point (−2,4)(−2,4): 4=a+14=a+1.

Solving this equation, we get that a=3a=3.

Thus, the equation of the parabola is y=3(x+3)2+1y=3(x+3)^2+1.

I used parabola calculator.

Hope it helps!