helpin a 120-volt circuit having a resistance of 12 ohms, the power W in watts when a current I is flowing through is given by W=120 I - 12 I^2....

The equation power w is given by
:

W = 120i - 12i^2

To find 
the maximum power W.

To
maximise W:

W/12 = (120i-12i^2)/12 =
10i-i^2

W/12 = 2*5i-i^2

W/12
=5^5  -5^2+2*5i-i^2

W/12 = 5^2 - (5 -
i)^2

W/12  <5^2 , as  (5-i)^2 being a perfect square
is always positive.

So the W/12 is maximum and equal to
5^2=25  when i = 5 amp.

Or the maximum power that could
drawn is  W = 25*12 = 300 watts, when i = 5amp.