The standard form of a parabola is



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



In this case (h,k) = (3,3),  so the above becomes



y = a(x - 3)² + 3



Since is contains the point (x,y) = (-2,53)



53 = a(-2 - 3)² + 3



53 = a(-5)² + 3



53 = a(25) + 3



53 = 25a + 3



50 = 25a



2 = a



Substitute 2 for a in



y = a(x - 3)² + 3



y = 2(x - 3)² + 3

 

That's the equation you were looking for.



The graph is





 

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