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,  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 

  x  = 2 and x = 4

Shown is y = 2(x-3)^2 - 2 as another possiblity



 

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