SOLUTION: Using {{{f(x)=(1/2)(x+4)^2+7}}}, find the vertex, the equation of the line of symmetry, and the max/min value of f(x).

Question 130759: Using , find the vertex, the equation of the line of symmetry, and the max/min value of f(x).
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Rewrite as

Now the equation is in vertex form where "a" is the stretch/compression factor and (h,k) is the vertex. So this means that , , and

So the vertex is (-4,7)

Now the equation of the line of symmetry is in the general form . So the equation of the line of symmetry is

Now since the vertex is where the max/min occurs, this means that the max/min of f(x) is the y-coordinate of the vertex. So the max/min of f(x) is 7
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