H(x) = −(x − 5)2 + 3 g(x) = 4 cos(2x − π) − 2 f(x) x y 0 −5 1 0 2 3 3 4 4 3 5 0 6 −5 which function has the largest maximum? answers:   f(x)  g(x)  h(x)  all three functions have the same maximum value.

The correct option is 1. The function f(x) has the largest maximum.

Step-by-step explanation:

The vertex form of a parabola is

Where, (h,k) is vertex.

The given functions is

Here, a=-1, h=-5 and k=3. Since the value of a is negative, therefore it is an downward parabola and vertex is the point of maxima.

Thus the maximum value of the function h(x) is 3.

The value of cosine function lies between -1 to 1.

Multiply 4 on each side.

Subtract 2 from each side.

Therefore the maximum value of the function g(x) is 2.

From the given table it is clear that the maximum value of the function f(x) is 4 at x=3.

Since the function f(x) has the largest maximum, therefore the correct option is 1.

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