Question

A projectile is launched from the ground at 128 feet per second and will hit the ground after a certain amount of time. It models the function g(x) = -16x2 + 128x, where x represents the time of the of the flight (in seconds) of the projectile. What is an appropriate domain for this model? 00 0

Answer 1

$g=-16x^2+128x$

time can only take values ​​greater than or equal to zero, so the domain starts on 0

the las point of the domain is when the projectile hit the ground, this means when g=0

now we will replace g=0 o find the last value of the domain

$\begin{gathered} g=0 \\ -16x^2+128x=0 \end{gathered}$

solve x to know the last time

$\begin{gathered} 16x(-x+8)=0 \\ -x+8=\frac{0}{16x} \\ -x+8=0 \\ -x=-8 \\ x=8 \\ \end{gathered}$

the last time in seconds of the model is 8

so the domain is

$\lbrack0,8\rbrack$