# How do you determine the intervals where f(x)=x^2-4x+7 is concave up or down?

Nov 27, 2016

See below.

#### Explanation:

The graph of $f$ is a parabola (because $f$ is a quadratic function) that opens upward (because $a$ is positive). So it is concave up everywhere.
$f ' ' \left(x\right) = 2$ is positive everywhere, so the graph of $f$ is concave up everywhere.