Parabolas, What does "b" do?

Question

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?

Answer 1

You can play with $a, b, c$ here:

http://www.mathwarehouse.com/quadratic/parabola/interactive-parabola.php

Generally, the the coordinates of vertex are $T(-\frac{b}{2a}, \frac{4ac-b^2}{4a})$.

Answer 2

It is true if $a \gt 0$. You can write it as $a(x+\frac {b}{2a})^2+c-\frac {b^2}{4a}$ The vertex is then at $x=-\frac b{2a}$

Answer 3

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 $x=\frac{-b}{2a}$.