Question

What is the axis of symmetry and vertex for the graph `f(x)= 2x^2 - 11`?

Answer 1

Vertex`->(x,y)=(0,-11)`

The axis of symmetry is the y-axis

Explanation:

First write as `" "y=2x^2+0x-11`

Then write as `" "y=2(x^2+0/2x)-11`

This is part of the process for completing the square.

I have written this format on purpose so that we can apply:

The value for `x_("vertex")= (-1/2)xx(+0/2)=0`

So the axis of symmetry is the y-axis.

So

`y_("vertex")=2(x_("vertex"))^2-11`

`y_("vertex")=2(0)^2-11`

`y_("vertex")=-11`

Vertex`->(x,y)=(0,-11)`

Answer 2

Axis of symmetry is `y`-axis

Vertex is at `(0,-11)`

Explanation:

From the equation given it is obvious that vertex is at `x=0 ,y=-11`.

and the axis of symmetry is `x=0` that is the `y`- axis.

There is no `x` term so the graph has not moved left or right, only down `11` units.