Question

Identify the vertex, axis of symmetry, and direction of opening for y=2(x+3)^2-5

y = |2x+3|^2-5
h = 3
k = -5

vertex = (3,-5)
axis of symmetry = x = 3
direction = up b/c a = 2 and 2>0

Answer 1

y = 2 (x+3)^2 - 5
(x+3)^2 = (1/2)(y+5)
(x+3)^2 = 4 (1/8) (y+5)
vertex (-3,-5)
symmetric about x = -3
indeed opens up because a = +1/8, check as x becomes very positive or very negative, y gets big positive

Answer 2

I don't understand what you did after the 1st line.

Answer 3

Hmmm
I know, and I bet it is in your book, that
a formula of type:
(x-h)^2 = 4 a (y-k)
is a parabola with vertex at (h,k)
a is the distance from vertex to focus and from vertex to directrix
if a is +, opens up. if a is -, opens down