Question

a model rocket is launched from the ground with an initial velocity of 60 feet per second. the function g(t)= -16t^2 + 60t represents the height of the rocket , g(t), t seconds after it was launched ... what is the absoloute max, zeros, domain, and range

Answer 1

If we use our trusty ti's this will be a breeze
domain is the numbers we can use
obviously we can't have negative time so therefor the domain is all positive integers (0,1,2,2.3, 3/2,3,pi...) 

zeroes is when you set absolute max using ti is
remember vertex form which is
max height of something in
ax^2+bx+c form is -b/2a
-16t^2+60t+0
a=-16
b=60
-60/(2 times -16)
-60/-32=30/16=15/8=1 and 7/8 so subsitute for t
g(15/8)=-16(15/8)^2+60(15/8)=225/4=56.25=max height


zeroes is when the equation equals 0
so set it to zero
0=-16t^2+60t
factor
0=(-4t)(4x-15)
set each to zero
-4x=0
x=0
4x-15=0
add 15
4x=15
divid 4
x=15/4
so the zeros are t=0 and t=15/4

domain is all the nuumbers that can be used logically for time
logically, we cannot have negative time, so all real positive
[0,∞)
(that means from 0 to infinity includng 0 so 0<t<∞))


range is the output
output=height
we find the min height and max height
min=0
max=56.25
so range=0 to 56.25 or
[0,56.25]






max height=56.25 ft (15/8 seconds)
zeroes=0 sec and 15/4 sec
domain=all real positive numbers including zero or [0, ∞)
range=[0,56.25]