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

f(x) = −8x2 + 7

x g(x)
0 0
1 2
2 6
3 2
4 0

which of the following statements best compares the maximum value of the 2 functions?

it 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.

For f(x)
The maximum value is determined by plotting the function or taking the derivative and equating it to zero.
So,
df(x)/dx = -8(2) x = 0
-16x = 0
x = 0

Testing if it gives a maximum, we take the second derivative:
d2f(x)/dx2 = -16
Since it's a negative number, x=0 give us a maximum value.
So,
f(0) = 0 + 7 = 7

For g(x), plotting the given points gives us the maximum value at x=2 and g(x) = 6

Comparing the two maximum values. We have,
f(x) has a greater maximum value than g(x).