Question 170: Is there a shortcut in determining where the y-coordinate of the vertex?
Answer by KMST(5483)   (Show Source):
You can put this solution on YOUR website! If you are faced with a quadratic function such as  ,
you should know that it will have a curved graph
that will look like the graph of  ,  ,
maybe stretched in one or another direction,
and/or shifted (moved, we like to say "traslated"),
and/or or flipped.
THE SHORTCUTS:
IF YOU GET LUCKY, the polynomial factors easily, as in  ,
and the roots of the polynomial are obvious,
like  and  for ,
Then you realize, that as quadratics graph as symmetrical curves (parabolas),
the x-coordinate of the vertex,  is at equal distance to both roots,
and can be calculated as their average, as in  .
YOU CAN MEMORIZE A FORMULA, such as  for 
or remember it as part of
that tells you that  would be the average of the 2 roots of the polynomial if the polynomial had real roots.
(This shortcut works even if there are no real roots).
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