Parabola focus

[rich oyster]

Hi does anybody know the demonstration to say that the vertex of a parabola is V(-b/2a ; -Delta/4a) ?

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[dreamy ledge]

Try completing the square in f(x) = ax^2 + bx + c.

[rich oyster]

oh yea my teacher did sometihhng like that to prove that ax^2 + bx + c=y was the equation of a parabola

[rich oyster]

wouldnt i just end up with a distance between the focus and a point being ewqual to the distance between the directrice and teh point?

[dreamy ledge]

No. That requires additional work.
If you complete the square, you'll just get f(x) = a(x - x0)^2 + y0, where (x0, y0) is the vertex.

[rich oyster]

how do i find -b/2a from there?

[dreamy ledge]

As I said, try completing the square in ax^2 + bx + c.