Question

What is the axis of symmetry and vertex for the graph `f(x) = 8 - (x+3)^2`?

Answer 1

The vertex is `(-3, 8)` and the axis of symmetry is `x=-3`

Explanation:

In order to find the vertex, you would have to expand the brackets, simplify all the terms and then complete the square.

Another method is instead of completing the square, a formula can be used instead: `x=b/(2a)`. This also gives the axis of symmetry.

Then we use the function to find `f(b/(2a))`, and this will give us the coordinates of the vertex.
graph{8-(x+3)^2 [-10, 10, -5, 5]}