As x gets very big positive or negative, T gets very small. In other words this parabola opens down (sheds water)
Where is the vertex (the top) ?
Complete the square
.005 x^2 - .45 x -123 = -T
x^2 - 90 x - 24600 = -200 T
x^2 - 90 x = -200 T +24600
x^2 -90 x + 2025 = -200 T + 26625
(x-45)^2 = -200 (T - 133.125)
so
vertex at (45 , 133.125)
so
It does not quite make 135 degrees
Now wait a minute, it never reaches 154 degrees.
during a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. the manufacturer of the machine recommends that the temperature of the machine part remain below 135 degrees. the temperature T in degrees fahrenheit x minutes after the machine is put into operation is modeled by T=-0.005x^2+0.45x+123
a. tell whether the temperature of the part will ever reach or exceed 135 degrees Fahrenheit. use the discriminant of a quadratic equation to decide.
b. if the machine is in operation for 90 minutes before being turned off, how many times will the temperature of the part be 154 degrees Fahrenheit?
1 answer
7 answers