Question

What is the axis of symmetry and vertex for the graph `y = 2(x + 7)^2 – 4`?

Answer 1

`color(blue)(" vertex "->" " (x,y) -> (-7,-4)`

`color(blue)(" axis of symmetry "->" "x=(-1)xx7=-7`

Explanation:

This is a quadratic transformed into Vertex Equation format.

The advantage of this format is that it needs very little work from this point to determine both the axis of symmetry and the vertex.

Notice from the graph that the axis of symmetry is `x=-7`
Now look at the equation and you will spot that this is the product of:

`color(blue)(" axis of symmetry "->" "x=(-1)xx7`

Also notice that the constant and this x-value form the coordinates of the vertex:

`color(blue)(" vertex "->" " (x,y) -> (-7,-4)`