Question

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

f(x) = −2x2 + 9


x g(x)
0 −5
1 3
2 11
3 3
4 −5


Which statement best compares the maximum value of the two functions?
The maximum value is the same for both functions.
f(x) has a greater maximum value than g(x).
g(x) has a greater maximum value than f(x).
The maximum values cannot be determined.

Answer 1

Answer:

The answer is C or the third option. "g(x) has a greater maximum value than f(x)"

Step-by-step explanation:

I took the test and got it correct.

Answer 2

The statement that best compares the maximum value of the two functions is g(x) has a greater maximum value than f(x).

How to compare both functions?

The function f is given as:

f(x) = -2x^2 + 9

Differentiate the function

f'(x) = -4x

Set to 0

-4x = 0

Divide both sides by -4

x = 0

Substitute x = 0 in f(x)

f(0) = -2(0)^2 + 9

f(0) = 9

This means that the maximum value of function f(x) is 9

From the table of function g(x), the maximum is 11

11 is greater than 9

Hence, g(x) has a greater maximum value than f(x).

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