Make up an equation that satisfies the given conditions: must have x-intercepts at (1,0) and (2,0). It must also have a y-intercept at (0,4). How do you factor the y-intercept?

from the two x-intercepts, I know it must look something like

y = (x-1)(x-2)
but it could also have been y = 4(x-1)(x-2),
same x-intercepts just stretched differently in the vertical.

so let it be
y = a(x-1)(x-2)
we want it to pass through (0,4)
thus:
4 = a(-1)(-2)
4 = 2a
a = 2

y = 2(x-1)(x-2)

The fact that (0,4) is a y-intercept didn't matter, I would have used the same method for any other given point

e.g. same as above, except the curve must pass through (3,8)
let the equation be y = a(x-1)(x-2)
for (3,8)
8 = a(2)(1)
2a = 8
a = 4

y = 4(x-1)(x-2)