Question 953079: Identify the axis of symmetry.
f(x) = x2 + 10x + 9
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443)   (Show Source):
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! 
You can see that
by adding  I "completed the square  .
Of course I add to also add  to compensate, so as not to change the equation.
(You may call that subtracting , but I prefer to see it as adding a negative number).
You can also see that opposite values for  give the same value to  .
In other words,
 and  result in the same  for any value of  .
That means that  <---> is the axis of symmetry.
Points that are a distance to either side of that line,
either with  <--> ,
or with  <--> ,
have the same  .
So, for every  ,
there will be a point     and
a point  ,
which is symmetrical, each being the reflection of the other point
to the other side of the line <--> .
There is only one point with <--> ,
and it has  . That is the point   .
Since all the other points have  ,
the point is the vertex and minimum of the graph of .
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