Question

what is the vertex and line symmetry for f(x)=1/2(x+8)^2+4 and what is the max/min value of f(x)?

Is the answer for the vertex (8,4)
is the min value of f(x) (-8,4)

Answer 1

The answer for the vertex is correct, but the value of the minimum is not.
Also, you have not yet found the line of symmetry.


The standard form of a quadratic is
f(x)=a(x-h)²+k
where (h,k) is the vertex.
If a>0, the parabola is concave upwards, so the minimum is the vertex.
If a<0, the parabola is concave downwards, and the maximum is the vertex.
The line of symmetry is a vertical line through the vertex, namely, x=k.

Answer 2

so the ine symmetry would be 8 and the min or max would be 4

Answer 3

so the ine symmetry would be 8 and the min or max would be 4

Answer 4

Actually, I made a mistake of the sign in the above response.

The equation is written as:
f(x)=a(x-h)²+k
so for
f(x)=1/2(x+8)^2+4
h=-8, and k=4

Therefore the vertex is at (h,k) = (-8,4), and the line of symmetry is at x=-8.
The minimum is at the vertex, namely (-8,4) as you suggested.