Question

What is the axis of symmetry and vertex for the graph `y=2(x+3)^2+6`?

Answer 1

Vertex is at `(-3 ,6)`. Axis of symmetry is `x= -3`

Explanation:

`y =2(x+3)^2+6`

Comparing with standard vertex form of equation

`y = a(x-h)^2 +k ; (h,k)` being vertex , we find here

`h = -3 . k =6` So Vertex is at `(-3 ,6)`.

Axis of symmetry is `x =h or x= -3`

graph{2(x+3)^2+6 [-40, 40, -20, 20]}

Answer 2

`x=-3,(-3,6)`

Explanation:

`"the equation of a parabola in "color(blue)"vertex form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`
where ( h , k ) are the coordinates of the vertex and a is a constant.

`y=2(x+3)^2+6" is in this form"`

`"with "h=-3" and "k=6`

`rArrcolor(magenta)"vertex "=(-3,6)`

`"the axis of symmetry passes through the vertex, is vertical"`

`"with equation "x=-3`