Answer:
Look down
Explanation:
To find the maximum value of the given function y = -6 + ½ sin^2(x), we need to determine the maximum value of sin^2(x).
The range of the sine function is between -1 and 1, inclusive. The squared value of any number between -1 and 1 will always be between 0 and 1, inclusive. Therefore, sin^2(x) will always be between 0 and 1.
Since the coefficient of sin^2(x) is positive, the maximum value of y will occur when sin^2(x) is at its maximum, which is 1. Hence, the maximum value of y can be found by substituting sin^2(x) = 1 into the function:
y = -6 + ½ * 1
y = -6 + ½
y = -6 + 0.5
y = -5.5
Therefore, the maximum value of the function y = -6 + ½ sin^2(x) is -5.5.