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.