Posted by eric on Monday, December 5, 2011 at 1:31pm.
A machine's ideal temperature is below 135 degreesF. The temperature T in degrees x minutes after it is turned on is T=0.005x^2 = 0.45x + 125. Will the temperature ever exceed 135 degrees. Use the discriminate to decide. If the machine operates for 90 minutes before being turned off, how many times will the temperature be 134 degrees?

algebra  Steve, Monday, December 5, 2011 at 2:52pm
assuming that you mean
T=0.005x^2 + 0.45x + 125
the max temperature is reached at x = .45/.01 = 45
so,
T(45) = 135.125
so, yes, the temperature does exceed 135, but only briefly (for 40<=x<=50)
Using the discriminant of
0.005x^2 + 0.45x + 125  135 = 0
D = .45^2  4*.005*10 = .0025
D>0, so yes, T will exceed 135
Since the equation is a parabola, there will be at most two times. Those are at
x = 30 and 60