SOLUTION: Aki's bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by c(x)=0.2x�-1.3x+8.181, where c(x) is in hundreds of dollars.

Question 633223: Aki's bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by c(x)=0.2x�-1.3x+8.181, where c(x) is in hundreds of dollars.
The shop should build_____bicycles.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
is a quadratic function.
As a quadratic function with a positive coefficient for the term in ,
it goes through a minimum.
Quadratic functions have the general form

They graph as parabolas,
and have a minimum or maximum at .
In the case of , there is a
minimum at --> -->
So the cost per bicycle is minimum when hundred bicycles are built.
That is

ABOUT QUADRATIC FUNCTIONS:
For a quadratic function, ,
when the leading coefficient, , is positive,
the function grows without bounds as increases on both ends (positive and negative),
as the term overwhelms whatever value the rest of the polynomial could take.
As a consequence the function looks like a smile, with a minimum in the middle:

If the shape of the graph is flipped and the function has a maximum:

The maximum or minimum is the vertex of the parabola.
The function can be transformed algebraically from to

which shows that the extreme value (maximum or minimum) occurs when
, when
and the line represented by is the axis of symmetry of the parabola that is the graph of the function.
If the expression reminds you of the quadratic formula, it is no coincidence.
The quadratic formula comes from the same
making .
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