Question

Write the equation of the quadratic function with roots 0 and 2 and a vertex at (1, 5).

Answer 1

Isn't this technically the same problem as that last one?

Roots 0 and 2 means if x=0 or 2, then y=0.
y=(x-0)*(x-2)
Vertex (1,5) means if x=1, then y=5.
5=a(1-0)*(1-2)
5=a*-1
a=-5

Answer: y=-5x(x-2)
Which is expanded to \[y=-5x^2+10x\]