Theorem QF.SHAPE (The shape of quadratic functions):
Case P(ositive and uP): If $A >0$ then there is a number $c$ where $f$ is an decreasing function for all $x\le c$ while $f$ is an increasing function for all $x\ge c$. ["bowl up"]
Case N(egative and dowN) If $A <0$ then there is a number $c$ where $f$ is an increasing function for all $x \le c$ while $f$ is an decreasing function for all $x \ge c$. ["bowl down"]
(The converses of each of these are also true for quadratic functions.)