Answer:
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.
