SOLUTION: Find the vertex, line of symmentry, and the max/min value of f(x)=1/5(x+2)^2+2, is the valuef(=2)=2 min or max and graph. I am having problems trying to solve this.

Algebra ->  Rational-functions -> SOLUTION: Find the vertex, line of symmentry, and the max/min value of f(x)=1/5(x+2)^2+2, is the valuef(=2)=2 min or max and graph. I am having problems trying to solve this.      Log On


   

Question 408202: Find the vertex, line of symmentry, and the max/min value of f(x)=1/5(x+2)^2+2, is the valuef(=2)=2 min or max and graph. I am having problems trying to solve this.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%281%2F5%29%2A%28x+%2B+2%29%5E2+%2B+2
I can say z+=+x+%2B+2, then
f%28z%29+=+%281%2F5%29%2Az%5E2+%2B+2
In an equation of the form
f%28z%29+=+a%2Az%5E2+%2B+b%2Az+%2B+c, the z-coordinate of
the vertex is at -b%2F%282a%29, but b+=+0
here, so (0,f(0)) is the vertex, and to find y
f%280%29+=+%281%2F5%29%2A0%5E2+%2B+2
The vertex is at (0,2)
Now I translate this to (x,f(x))
z+=+x+%2B+2
0+=+x+%2B+2
x+=+-2
f%28-2%29+=+%281%2F5%29%2A%280%29%5E2+%2B+2
f%28-2%29+=+2
(x,f(x)) = (-2,2)
The line of symmetry is x+=+-2
The graph is a min at f%28x%29+=+2
Here is the plot:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F5%29%2A%28x+%2B+2%29%5E2+%2B+2%29+