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).

Algebra ->  Quadratic Equations and Parabolas -> 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).      Log On


   

Question 130759: Using f%28x%29=%281%2F2%29%28x%2B4%29%5E2%2B7, find the vertex, the equation of the line of symmetry, and the max/min value of f(x).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%281%2F2%29%28x%2B4%29%5E2%2B7 Start with the given equation


f%28x%29=%281%2F2%29%28x-%28-4%29%29%5E2%2B7 Rewrite x%2B4 as x-%28-4%29


Now the equation is in vertex form y=a%28x-h%29%5E2%2Bk where "a" is the stretch/compression factor and (h,k) is the vertex. So this means that a=1%2F2, 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