How do you find the axis of symmetry, and the maximum or minimum value of the function #f(x)=-4(x+1)^2+1#?

1 Answer
May 20, 2017

See below.

Explanation:

The axis of symmetry of a parabola occurs at its vertex, and if the parabola is not rotated, it is just the vertical line through the vertex.

The vertex is #(-1,1)#, so the axis of symmetry is #x=-1#.

A parabola has a minimum if #a# is positive in #y=a(x-h)^2+k#, and a maximum if #a# is negative. In this case, #a=-4#, so there will be a maximum.

The maximum also occurs at the vertex, so the maximum value of this graph is #1# (the #y#-coordinate value)