Hi, can anyone help to:

determine the equation of a parabola with the vetex (0,3) and passing through (3,4)?
How to figure out the coeffiecient of X?

Certainly! To determine the equation of a parabola, we can use its vertex form, which is given by:

y = a(x-h)^2 + k

Here, (h, k) represents the coordinates of the vertex. In this case, the vertex is given as (0,3), so we can substitute these values into the equation:

y = a(x-0)^2 + 3
y = ax^2 + 3

Next, we need to find the coefficient "a" by using the fact that the parabola passes through the point (3,4). We substitute these coordinates into the equation and solve for "a":

4 = a(3)^2 + 3
4 = 9a + 3
9a = 1
a = 1/9

So, the coefficient of the x-term is 1/9. Therefore, the equation of the parabola is:

y = (1/9)x^2 + 3