Question

f(x)=1/2(x+5)^2+5: find the vertex, line of symetry and the max/min

Answer 1

vertex is
\[(-5,5)\] because this is in the form
\[f(x)=a(x-h)^2+k\] so you can read off the vertex from the equation

Answer 2

since the leading coefficient is positive, this is a parabola that opens up, so it has no maximum but the minimum is the second coordinate of the vertex, namely 5

Answer 3

axis of symmetry is what you get when
\[(x-5)^2=0\] namely
\[x=5\]