In each of the, find the equation of the parabola that satisfies the given conditions:

Vertex (0, 0) passing through (2, 3) and axis is along x-axis.

Since, the vertex is (0, 0) and the axis of the parabola is the x-axis, the equation of the parabola is either of the from y²=4ax or y² = -4ax.

The parabola passes through point (2, 3), which lies in the first quadrant.

Thus, the equation of the parabola is of the form y² = 4ax, while point (2, 3) must satisfy the equation y² = 4ax.

Thus,

3² = 4a(2)

⇒ a = 9/8

Thus, the equation of the parabola is

⇒ 2y² = 9x