How do you find the vertex of #f(x)=-(x-1)^2+2#?

1 Answer
Oct 4, 2016

Vertex: #(1,2)#

Explanation:

An equation in the form #f(x)=color(green)(m)(x-color(red)(a))^2+color(blue)(b)#
is in vertex form with vertex at #(color(red)(a),color(blue)(b))#

#f(x)=-(x-1)^2+2#
is equivalent to
#f(x)=color(green)(""(-1))(x-color(red)(1))^2+color(blue)(2)#
and therefore has a vertex at #(color(red)(1),color(blue)(2))#

Here is a graph of the original equation for verification purposes:
graph{-(x-1)^2+2 [-2.507, 3.652, -0.54, 2.537]}