Question 534305
<pre>
The standard form of a parabola is

 y = a(x - h)² + k

where the vertex is (h,k)

Substitute (h,k)= (2,3),  (x,y) = (0,2) into 
the standard form:

 y = a(x - h)² + k

 2 = a(0 - 2)² + 3

 2 = a(-2)² + 3

 2 = a(4) + 3

 2 = 4a + 3

-1 = 4a

{{{(-1)/4}}} = a

{{{-1/4}}} = a

Substitute a = {{{-1/4}}}, h = 2, k = 3 in

 y = a(x - h)² + k

 y = {{{-1/4}}}(x - 2)² + 3

 {{{drawing(400,2000/9,-8,10,-5,5,

graph(400,2000/9,-8,10,-5,5,(-(x-2)^2)/4+3),
circle(2,3,.15), locate(2+.4,3+.5,"(2,3)"),
circle(0,2,.15), locate(0+.4,2+.5,"(0,2)") )}}}

Edwin</pre>