# Math Help - A rocket is launced upward..

1. ## A rocket is launced upward..

A rocket is launched upward from the top of a 30-foot tall platform. The height of the rocket in feet, $h(t)$, at time $t\geq0$, is given by the equation $h(t)= -16t^2+256t+30$

a) At what time is the rocket at a maximum height?

b) What is the maximum height in feet that the rocket can reach?

Can you show me how to do these?

2. This problem is really asking about the coordinates of the vertex. The x-coordinate of the vertex represents time (t) and the y-coordinate represents height (h).

To find the x-coordinate of the vertex of a quadratic of the form $y=ax^2 + bx + c$, use:

$x=- \frac{b}{2a}$.

Once you've found the x-coordinate, that represents the time at which the object reaches its highest point. To find the height AT THAT TIME, simply plug in the x-coordinate to your equation (for t) and you'll get out the height.