Question 391360
  <pre><font size = 3 color = "indigo"><b>
Hi
quadratic equation intersects the x axis at (2,0) and (4,0)
that tells us the  vertex is at (3,k)
the vertex form of a parabola, {{{y=a(x-h)^2 +k}}} where(h,k) is the vertex
y = a(x-3)^2 + k   |using Pt(2,0) for reference
0 = a + k
-a = k
y could equal = (x-3)^2 - 1   green parabola
 y = x^2 - 6x + 9 - 1
 y = x^2 -6x + 8
value of the discriminant could be {{{  b^2-4*a*c = 36 -32 = 4 }}}
{{{x = (6 +- 2)/2 }}}  x  = 2 and x = 4
Shown is y = 2(x-3)^2 - 2 as another possiblity
{{{drawing(300,300, -6, 6, -6, 6, blue(line(3,6,3,-6)),    grid(1),
circle(2, 0,0.3),
circle(4, 0,0.3),
graph( 300, 300, -6, 6, -6, 6,0,(x-3)^2 - 1,  2(x-3)^2 - 2))}}}