Given the functions f(x) and g(x), which of the following statements is true
x | -2 -1 0 1 2
f(x)| -3 3 5 3 -3
g(x) = -x^2 +4
statements:
f(x) has the greater maximum.
g(x) has the greater maximum.
f(x) and g(x) have the same maximum.

f(x) has the greater maximum ⇒ 1st statement

Step-by-step explanation:

* Lets explain how to solve the problem

- The quadratic function represented graphically by a parabola with

 minimum point or maximum point

- If the parabola is opened upward then its vertex is minimum, and is

 it is opened downward then its vertex is maximum

- The form of the quadratic function is f(x) = ax² + bx + c, where

  a , b , c are constant

- The vertex of the parabola is (h , k), where h = -b/2a and k = f(h)

- The vertex of the parabola is minimum if a is positive and maximum

 if a is negative

* Lets solve the problem

∵ The graph of f(x) has the points (-2 , -3) , (-1 , 3) , (0 , 5) , (1 , 3) , (2 , -3)

∵ The vertex of the parabola has the greatest value of y when it's

  opened downward

∵ The x-coordinate of the vertex point is at half the distance between

 each two x-coordinates of the opposite points

∵ The point (0 , 5) has the greatest y-coordinate

∵ Its x-coordinate = (-1 + 1)/2 = 0 or (-2 + 2)/2 = 0

∴ The vertex of f(x) is (0 , 5)

∴ The maximum value of f(x) is 5

∵ g(x) = -x² + 4

∵ The general form of g(x) = ax² + bx + c

∴ a = -1 , b = 0 , c = 4

- Lets calculate the x-coordinate of the vertex point using the

 rule above

∵ h = -b/2a

∴ h = 0/2(-1) = 0

∵ k = g(h)

∴ k = g(0) = -(0)² + 4 = 4

∴ The vertex of g(x) = (0 , 4)

∵ a is negative , then the vertex point is maximum

∴ The maximum value of g(x) is 4

∵ The maximum value of f(x) is 5 and the maximum value of g(x) is 4

∴ f(x) has the greater maximum.

step-by-step explanation: