How do you find the vertex of a parabola #f(x) = -x^2 + 2x + 5#?

1 Answer
Jul 8, 2015

Vertex is at #(1,6)#

Explanation:

A function expressed in the form
#color(white)("XXXX")##f(x) = m(x-a)^2+b# is in "vertex form" with its vertex at #(a,b)#

One way of determining the vertex of a parabolic function is to convert it into "vertex form".

#f(x)=-x^2+2x+5#
#color(white)("XXXX")#extract #m#
#f(x) = (-1)(x^2-2x)+5#
#color(white)("XXXX")#complete the square
#f(x) = (-1)(x^2-2x+1) + 5 -(-1)(1)#
#color(white)("XXXX")#simplify into vertex form
#f(x) = (-1)(x-1)^2+6#
#color(white)("XXXX")#read the vertex coordinates from the form
Vertex is at #(1,6)#