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

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 $\left(- 1 , 1\right)$, so the axis of symmetry is $x = - 1$.

A parabola has a minimum if $a$ is positive in $y = a {\left(x - h\right)}^{2} + k$, 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)