Question

Functions f(x) and g(x) are shown below:

f(x) = -4(x - 6)^2 + 3

g(x) = 2 • cos(2 • x - pi) + 4


Using COMPLETE SENTENCES, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.

Answer 1

Consider f(x) = -4(x - 6)² + 3
This is a parabola with vertex at (6, 3).
Because the leading coefficient of -4 is negative, the curve opens downward, and the vertex is the maximum value.

Answer: Maximum of f(X) = 3

Consider the function g(x) = 2 cos(2x - π) + 4
The maximum value of the cosine function is 1.
Therefore the maximum value of g(x) is
2*1 + 4 = 6

Answer: Maximum of g(x) = 6