Hello, epetrik!

Here is a non-Calculus solution . . .An object is thrown from the origin of a coordinate system

with the x-axis along the ground and the y-axis vertical.

Its path, or trajectory, is given by the equation: .

Find the object's maximum height.

The path is a down-opening parabola; its maximum is at itsvertex.

The vertex of the parabola, , is at: .

We have: .

. . The vertex is at: .

Then: .

The maximum height is about: units.