Question

a model rocket is launched into the air from ground level. the height, in feet, in feet, is modeled by p(x)=16x^2+32x, where x is the number of elapsed seconds. what is the total number of seconds the model rocket will be in the air?

Answer 1

Since you are given the function for the height of a rocket, we are to look for the value of X that gives us a value of p(x) = 0, which means that the model rocket has landed back onto the ground. One easy way to do this is by table method, meaning we substitute values of x to see if we can obtain the needed value of P(x). We should start from 1, since using 0 as our first value means that the rocket has not even launched up yet. Let us do this below:

x | p(x) = -16x^2+32x
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1 | p(1) = -16(1)^2 + 32(1) = 16
2 | p(2) = -16(2)^2 + 32(2) = 0

Having obtained the desired result at x = 2, this means that the model rocket has been in the air for 2 seconds.