Question

How do I find the vertex, axis of symmetry, y-intercept, x-intercept, domain and range of `y=2(x+3)^2+6`?

Answer 1

Vertex (-3,6),axis of symmetry x= -3,domain is R(set of real numbers) and Range is [6,infinite) graph{2(x+3)^2 +6 [-25.09, 20.51, -2.37, 20.43]}

Explanation:

On simplifying the equation,we have `(y-6)/2` = `(x+3)^2`
which represents a parabola.
Using `(y-6)/2` = `0`,y=6
and `(x+3)^2` = 0,x=-3
Thus,vertex of parabola is `(-3,6)`
Moreover,it is symmetric about its axis `x+3=0`