Polynomial Functions And Quadratic Models Worksheet - Lecture 6, University Of Florida Page 12
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Now You Try It!
1. Sketch the graph of the quadratic function f (x) =
x
4x + 3 by writing in
standard form and using translations.
2. Sketch the graph of f (x) = 3x
2x
5. Find the vertex and all intercepts.
3. A new action figure is sold at a local chain of toy stores. The district manager
observes that an average of 170 figures will sell per month when the selling price
is $7, but a price increase of $3 results in an average drop in sales of 30 per
month.
(a) Using a linear model, express price p as a function of the number of figures
sold in a month, x.
(b) Find the revenue function R(x). Find the price that should be charged to
maximize revenue. What is the maximum revenue?
(c) Fixed costs are $750 and it costs $4 to manufacture each figure. Find each
production level at which the manufacturer will break even.
(d) For what production levels will the manufacturer earn a profit? How many
should be sold to maximize profit?
4. Farmers in a certain community are earning $8 per bushel for their potatoes
on September 10, at the peak of the harvest season. But as more are brought
to market, price drops by 5 cents per bushel per day. On September 10, a
farmer has 140 bushels of potatoes in one field, and he estimates that the crop is
increasing by an average of one bushel per day. Express the farmer’s revenue as
a function of the number of days after September 10 until he harvests his crop.
When should he harvest the potatoes in order to maximize his revenue?
5. Consider the polynomial sketched below. If the leading coefficient is ax , find
the sign of a and the smallest possible value of n.
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