Question

What is the axis of symmetry and vertex for the graph `y= -x^2 + 1`?

Answer 1

Axis of symmetry is `x=0` (`y`-axis) and vertex is `(0,1)`

Explanation:

The axis of symmetry of `(y-k)=a(x-h)^2` is `x-h=0` and vertex is `(h,k)`.

As `y=-x^2+1` can be written as

`(y-1)=-1(x-0)^2`

hence axis of symmetry is `x-0=0` i.e. `x=0` (`y`-axis) and vertex is `(0,1)`

graph{-x^2+1 [-10.29, 9.71, -6.44, 3.56]}

Note: The axis of symmetry of `(x-h)=a(y-k)^2` is `y-k=0` and vertex is `(h,k)`.