How does the change in $b$ in the quadratic formula $ax^2+bx+c$ move the parabola in an inverted version of the quadratic function?
I've been using Desmos and trying to figure out the roles of the different terms in the quadratic equation $ax^2+bx+c$ the (ax) and the (c) term affect the parabola the way I thought it would, but the (bx) term affects it in a strange way that I can't quite understand. It seems to move the parabola along an inverted version of the same parabola.
I've seen people say that you can show the effect of the (bx) term by completing the square but when I look at the completed square I'm not sure how it shows what I want to know.
If you could complete the square for me and then explain how the end result shows how the (bx) term affects the parabola it would be of great help.
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