Converting Standard to Vertex Form (Parabolas)?

Hi i would like to know how you convert a Standard Parabola (y = ax^2 +bx + c) equation into a Vertex Parabola Form (y = a(x-h)^2 +k)

Converting Standard to Vertex Form (Parabolas)?
when converting from standard to vertex form you have to use completing the square.


if you had the equation


y= -x^2+6x - 8


you want the coefficient of the x^2 term to equal one, so that


y= - (x^2 - 6x) - 8


then you take half of the coefficent of the x term and square it and add and subtract it within the parentheses


y= - (x^2 - 6x + 9 - 9) - 8


regroup terms


y= - (x^2-6x+9) - (-9) - 8


simplify


y= - (x-3)^2 +1


and that is vertex form y= -1 (x-3)^2 +1





where (3,-1) equals the vertex