Find an equation of a parabola having its vertex at (0,0) and x-axis as its axis passing through the point (2,4).

Since the vertex is at (0,0) and the x-axis is the axis of the parabola, the equation of the parabola can be written in the form:

y = ax^2

To find the value of 'a', we can substitute the point (2,4) into the equation:

4 = a(2)^2
4 = 4a
a = 1

Therefore, the equation of the parabola is:

y = x^2

Since the vertex is at (0,0) and the axis is the x-axis, the equation of the parabola is of the form y^2 = 4ax.

To find the value of a, we can substitute the point (2,4) into the equation:

4^2 = 4a(2)
16 = 8a
a = 2

Therefore, the equation of the parabola is y^2 = 8x.