Help with Algebra 2/Trigonometry problem

[daodude1987]

I'm having trouble with proving this equation: x=-b\2a
I am not really familiar with this equation but my trigonometry teacher says it is something from Algebra 2. How can I prove why or how this equation works for finding the x-coordinate?

[HallsofIvy]

What do you mean "prove it"? It's an equation- its sometimes true and sometimes not. I suppose you mean "prove it is true for this particular situation" but you haven't told us what the situation is.
Could you please state the entire problem exactly?

[StephenPrivitera]

Using simple calculus, you can show that x=-b/2a is the point at which a parabola attains a minimum or maximum.
The vertical line x=-b/2a that goes thru this point is the axis of symmetry.

[HallsofIvy]

Ah! Thanks, Stephen, I recognized "-b/(2a)" as part of the quadratic formula but didn't recognize that he was asking for a proof that the x coordinate of the vertex of the parabola y= ax2+ bx+ c is -b/(2a).

[hawaiidude]

wait isn't -b/2a the vertex of a parabola? i kinda of forgot this but i think you can the coeficients of b and a get the vertex of the parabola

[HallsofIvy]

Yes, that was what StephenPrivitera told you!

[hawaiidude]

o sorry i only saw the oroginal question