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<span><</span>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]
So, to get 3 to 4, you would have to multiply 3 by something to get to 4. So you would divide 4 by 3 and get 1.3. So then you would divide 5 by 1.3 to solve for k, since k times 1.3 equals 5.
