Chapter 4 - Applications of the Derivative - 4.2 What Derivatives Tell Us - 4.2 Exercises - Page 259: 100

$f$ is concave up for $a > 0$ and concave down for $a < 0$.

$f'(x) = 2ax + b$, and $f''(x) = 2a$. Note that $f''(x)$ is positive for $a > 0$ and negative for $a < 0$. So $f$ is concave up for $a > 0$ and concave down for $a < 0$.