Question 356349
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Hi,
parabola passes through(2,0), (3,0) and (0,3). 

PT(2,0)and PT(3,0) tells us the axis of symmetry is x = 2.5 and 2.5 is the x value of the vertex

y = a(x-2)(x-3)
3 = a*6
1/2 = a
{{{y= a(x-h)^2 +k}}}   (h,k) is the vertex
{{{y = (1/2 )(x - 2.5)^2 + b}}}
(3,0)
0 = 1/2 * 1/4 + b
b = -1/8
y = .5(x-2.5) -1/8

{{{drawing(300,300,-10,10,-10,10,circle(2, 0,0.2),
circle(3, 0,0.2),
circle(0, 3,0.2),
blue(line(2.5,10,2.5,-10)),grid(1),graph(300,300,-10,10,-10,10, .5(x-2.5)^2 -1/8))}}}