Question

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

Answer 1

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)