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 2 functions?
1) it is the same for both functions
2) f(x) has a greater maximum value than g(x)
3) g(x) has a greater maximum value than f(x)
4) the maximum values can not be determined

option: 3 is true.

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

Step-by-step explanation:

We are given quadratic function f(x) as:

and quadratic function g(x) as:

xg(x)

0   −5

1   3

2   11

3    3

4   −5

From the graph of the function f(x) we see that the maximum value attained by the function is 9 when x=0.

Also it could be seen that x^2 is always positive when x≠0.

Hence, the maximum value of f(x) is 9.

Also from the set of values of function g(x) the maximum value attained by g(x) is 11.

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

1. perpendicular

2. parallel

3. perpendicular