Question 130759
{{{f(x)=(1/2)(x+4)^2+7}}} Start with the given equation



{{{f(x)=(1/2)(x-(-4))^2+7}}} Rewrite {{{x+4}}} as {{{x-(-4)}}}



Now the equation is in vertex form {{{y=a(x-h)^2+k}}} where "a" is the stretch/compression factor and (h,k) is the vertex. So this  means that {{{a=1/2}}}, {{{h=-4}}}, and {{{k=7}}}



So the vertex is (-4,7)


Now the equation of the line of symmetry is in the general form {{{x=h}}}. So the equation of the line of symmetry is {{{x=-4}}}



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