How come with (3,4) (vertex), and (1,2) (point) a doesn't equal -4.5, but -.5?

Question

Please show me how to get this answer.

Answer 1

Took me a bit to figure out what you are asking.
I think you are dealing with the general equation of a parabol in the form
y = a(x-h)^2 + k, where (h,k) is the vertex

so with vertex (3,4) our equation is
y = a(x-3)^2 + 4
sub in the other point (1,2)
2 = a(-2)^2 + 4
-2 = 4a
a = -2/4 = -1/2 = -0.5