# A rocket is launced upward..

• Jun 12th 2008, 06:00 PM
eh501
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, $\displaystyle h(t)$, at time $\displaystyle t\geq0$, is given by the equation $\displaystyle h(t)= -16t^2+256t+30$

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?
• Jun 12th 2008, 06:45 PM
Mathnasium
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 $\displaystyle y=ax^2 + bx + c$, use:

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

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.