The cost in dollard, of operating a machine per day is given in the formula C=3t^2 -96t +1024 , where t is the time the machine operates, in hours. What is the minimum cost of running the machine? for how many hours must the machine run to reach the minimum cost? PLEASE ANSWER IN COMPLETE THE SQUARE METHOD

Question

jdoe0001 · Answer

have you covered parabolas yet?

gazela1997 · Answer

YES

jdoe0001 · Answer

so notice the equation, is a parabola
the leading term has a POSITIVE coefficient, meaning if you make C= y or f(x)
then the parabola is going upwards, that is|dw:1402958227815:dw|  

so the minimum cost the machine can incur is likely 0, meaning you simply leave the machine idle =)   of course, there's an assumption that machine is working and the cost is just  the lowest at some point

that point will be at the "vertex" of the parabola

at that point, at those coordinates, COST will be the minimum and HOURS or time, will be how many it took to reach that point

gazela1997 · Answer

I know this but how do I carry out the equation?

gazela1997 · Answer

thats the part im stuck on. I did it with calculus and got the right answer but cant figure it out with completing the square.