This quadratic equation is in standard form, which is y(x) = ax2 + bx + c. By comparing the equations, we can see that t is the x (independent) variable and h is the y (dependent) variable. We can also see that a is -16, b is 64, and c is 64.
In general, the graph of a quadratic function is a parabola. Because a is negative, the parabola will open downward. The x-coordinate of the vertex is -b/(2a), which in this case is -64/(2*-16) = 2. By plugging that value of x into the equation, we get h(t) = 128, which is the y-coordinate of the vertex, so the vertex is the point (2,128). Once you know the vertex and which direction the parabola opens, you can make a rough sketch of it.
There is much more that you can do with quadratic equations, but I hope that this helps you with some of the basics.