Question

The quadratic functions f(x) and g(x) are described as follows:

f(x) = -4x2 + 5

Which of the following statements best compares the maximum value of the two functions?

A: The maximum value is the same for both functions.
B: f(x) has a greater maximum value than g(x).
C: g(x) has a greater maximum value than f(x).
D: The maximum values cannot be determined.

Answer 1

The true statement is (a) the maximum value is the same for both functions.

How to determine the true statement?

The function f(x) is given as:

f(x) = -4x² + 5

Rewrite as:

f(x) = -4(x - 0)² + 5

The vertex of a quadratic function of the form f(x) = a(x - h)² + k is:

Vertex = (h,k)

So, we have:

Vertex = (0,5)

This means that the maximum of the function f(x) is 5

From the table, the maximum of the function g(x) is also 5

Hence, the true statement is (a) the maximum value is the same for both functions.

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Answer 2

Answer: The maximum value is the same for both functions.

Step-by-step explanation: