Let
be the number of
increases in price and
be the income.
For each
increase in price, they will rent
fewer videos.
The store rents
videos per week at
.
If they increase the rent for every
increase, they will rent
fewer videos.
So the income
is
.
Hence the quadratic function is
.
The standard form of quadratic function
, where
.
and
.
Since
, the function has a maximum value and opens down.
The equation of the axis symmetry is
.
(Substitute the values
and
)
(Simplify)
The equation of the axis symmetry is
and
-coordinate of the vertex is
.
Find the maximum price income the store at
.
(Substitute
)
(Multiply)
(Substitute:
)
The maximum price is
income of the store.
The maximum price is
income of the store.