Calculate parameters of a parabola with SageMath

Question

I would like to use SageMath to solve some equations of combined/composite curves. However, I did not find a way to solve even a simple parabola so far. Here is the most simplified code I can think of:

x, a  = var('x a')
y(x) = a * x^2
solve([y, y(0)==0, y(1)==0.5], a)

Can be executed here: https://sagecell.sagemath.org/

Can someone say what is wrong and why I am not getting any result?

Answer 1

Delete the first y in the list:

sage: var('x a')
(x, a)
sage: y(x) = a*x^2
sage: solve([y(1) == 0.5, y(0) == 0], a)
[[a == (1/2)]]