The temperature y (in degrees Fahrenheit) after t months can be modeled by the function y=−2t^2+28t −16, where 1≤t≤12.

Question

The temperature y (in degrees Fahrenheit) after t months can be modeled by the function y = −2t^2+28t −16, where 1 ≤ t ≤ 12.

a. Write the function in vertex form.

Find the maximum temperature during the year.

Answer 1

y = -2t^2 + 28t - 16

= -2(t^2 - 14t) - 16

= -2(t^2 - 14t + 49) - 16 + 98 <--- completes the square: adding 49 *-2 = -98 inside parenthesis

= -2(t-7)(t-7) + 82

= -2(t - 7)^2 + 82

max temp when t=7 is 82 degrees