Chapter 3 - Quadratic Functions - 3.1 Introduction to the Family of Quadratic Functions - Exercises and Problems for Section 3.1 - Exercises and Problems - Page 121: 31

The graph of $f(x)$ opens downward and is concave down.

From the points given, we know that $f(x)$ increases from $x=1$ to $x=2$ because the values of $y$ increases from 2 to 4 on the interval and decreases from $x=3$ to $x=5$ because the value $y$ decreases from 4 to 2. Only a parabola opening downward increases and then decreases. Thus, the graph of $f(x)$ opens downward and is concave down.