Comparing Function Average with Function Value

Let the function f(x) be defined as follows:

$$f(x) = ax^2 + bx + c$$

where a, b, and c are constants with a > 0. Three different values for x are chosen:

• x = 1
• x = 2
• x = 3

Let Q1 be the average of the function values at these three points:

$$Q1 =\frac{f(1) + f(2) + f(3)}{3}$$

Let Q2 be the value of the function at the average of these points:

$$Q2 = figg(\frac{1 + 2 + 3}{3}igg) = f(2)$$

Which of the following statements is true regarding the relationship between Q1 and Q2?