shortcut using -b/2a....what was it used for?

[bamakathy]

I remember my professor teaching us a shortcut using -b/2a which was an easy way to find something....but I forgot when I used it. Can anyone help? Thanks, Kathy (old woman trying to remember her algebra)

 

[Mrspi]

I remember my professor teaching us a shortcut using -b/2a which was an easy way to find something....but I forgot when I used it. Can anyone help? Thanks, Kathy (old woman trying to remember her algebra)

It might have helped us if we knew what kind of problem you are working on, and in what context you are thinking of "-b/2a"

That said....

If you have a quadratic function in the form

y = ax[sup:19zurgue]2[/sup:19zurgue] + bx + c

the graph of this function is a PARABOLA.

It is often useful to find the vertex (maximum or minimum point) of the parabola.

it happens (and I think you should review WHY this is true!) that the x-coordinate of the vertex of a quadratic function is x = (-b)/(2a)

Is that what you were thinking of?

 

[bamakathy]

Yes, it was the vertex of the parabola! Of course! I remember the professor showing us the long way, and then saying...and there's a shortcut, and showed us how it worked. I've been helping my son with College Algebra, and just got this shortcut in my mind and couldn't remember what I used it for. Thanks so much.
Kathy

 

[mmm4444bot]

Yes, it [is] the [x-coordinate of the] vertex of the parabola …

If your son needs a way to remember -b/(2a), then here's my way.

-b/(2a) is what's left after removing the ±radicals from the Quadratic Formula.

\(\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)