Question 550954
write the equation of the parabola in vertex form: vertex (3,3) that goes through the point (-2,53).
<pre>
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

{{{drawing(400, 500,-3,10,-2,60,
circle(-2,53,.1), locate(-3,53,"(-2,53)"),circle(3,3,.1), locate(3,3,"vertex(3,3)"),

graph(400, 500,-3,10,-2,60,2(x-3)^2+3) )}}}