SOLUTION: Find the vertex, line of symmetry, maximum/minimum value and then graph the function. f(x) = 1/2 (x+4)^2 + 6 I'm thrown off by the fractions, and the whole equation. Can som

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Find the vertex, line of symmetry, maximum/minimum value and then graph the function. f(x) = 1/2 (x+4)^2 + 6 I'm thrown off by the fractions, and the whole equation. Can som      Log On

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Question 133003: Find the vertex, line of symmetry, maximum/minimum value and then graph the function.
f(x) = 1/2 (x+4)^2 + 6
I'm thrown off by the fractions, and the whole equation. Can someone help me figure out how to solve this type of problem.
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(16868) About Me  (Show Source):
You can put this solution on YOUR website!
I would love to help, but how much of that mess is in the denominator? Just the 2? The 2(x+4)^2? or is does it look like this: f%28x%29+=+1%2F%282+%28x%2B4%29%5E2+%2B+6%29?

Answer by jim_thompson5910(28504) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%281%2F2%29+%28x%2B4%29%5E2+%2B+6 Start with the given equation


f%28x%29+=+%281%2F2%29+%28x-%28-4%29%29%5E2+%2B+6 Rewrite x%2B4 as x-%28-4%29


Notice how the equation is now in vertex form y=a%28x-h%29%5E2%2Bk where a=1%2F2, h=-4 and k=6


Remember, the vertex is (h,k). So in this case the vertex is (-4,6).

The line of symmetry is in the form x=h. So the equation is x=-4


Since a%3E0 (ie it's positive), the parabola opens up. So this means that a min will occur at the vertex. So in this case the minimum is y=6





If we graph the function, we can visually verify our answer.


Graph of f%28x%29+=+%281%2F2%29+%28x%2B4%29%5E2+%2B+6 with the axis of symmetry x=-4 (blue line) and the vertex (-4,6)