What is the vertex of #y=x^2-6x+15#?

1 Answer
Jan 6, 2016

Vertex is at #(3,6)#

Explanation:

The general vertex form of a parabola is
#color(white)("XXX")y=m(x-color(blue)(a))^2+color(blue)(b)# for a parabola with vertex at #(color(blue)(a,b))#

Converting #y=x^2-6x+15# into this form:

Complete the square:
#color(white)("XXX")y=x^2-6xcolor(red)(+3^2) + 15 color(red)(-3^2)#
Re-write as a squared binomial
#color(white)("XXX")y=(x-color(blue)(3))^2+color(blue)(6)#
which is in the vertex form (with #m=1#) for a parabola with vertex at #(color(blue)(3,6))#