Parabolas, What does "b" do? Given a quadratic,
$ax^2+bx+c$.
I know c is the intercept, and the sign of $a$ tells us wether it is a positive "u" shape, or negative, an upside down u. But what about b? Is my following observation correct;
If b>0 the min or max is to the left of the y axis
If b<0 the min or max is to the right of the y axis?
Are these statements true?

If $b=0$ the graph of $y=ax^2+bx+c$ is symmetric with respect to the $y$ axis, if $b \ne 0$ it is symmetric with respect to the stright line $x=\frac{-b}{2a}$.
