parabola graph calculus

Question

What is the equation of the parabola shown in the graph?

Answer 1

Parabola equation:

y = a(x-h)²+k

Looks liked the vertex is (0,0), so h=k=0

y(0) = 0

y(1) = 1/2

y(2) = 2

y(3) = 4.5

So a = y(x)/x²

a = y(2)/2² = 2/4 = 1/2

y = x²/2