**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.*)