a.
The objective is to write a polynomial function to model the cost of purchase.
The polynomial function is
Given information:
Cost of cherries is $1 more per container than blueberries.
Cost of blueberries is $1 more per container than strawberries.
The product of all 3 prices is 5 times the total cost.
One container of each has been purchased.
Calculation:
Let the price of one container of strawberries be x .
Then, cost of a container of blueberries will be
According to the given information,
Simplify and solve for x .
Hence, the required polynomial function is
b.
To graph: The polynomial function
The price of strawberries per container is $3.
The price of blueberries per container is $4.
The price cherries per container is $5.
Given statement:
Cost of cherries is $1 more per container than blueberries.
Cost of blueberries is $1 more per container than strawberries.
The product of all 3 prices is 5 times the total cost.
One container of each has been purchased.
Explanation:
Create table for values of x and y .
x | |
-5 | 0 |
-2 | 15 |
-1 | 0 |
0 | -15 |
1 | -24 |
2 | -21 |
3 | 0 |
Plot points on the graph and join them.
From the graph, the possible values of
Since price cannot be negative.
Thus,
Hence, Cost of strawberries per container is $3.
Cost of blueberries per container is $4.
Cost of cherries per container is $5.
c.
To explain: The use of graph to find the prices.
Find the value of x where the graph intersects the x -axis and choose the positive values of x only as price cannot be negative.
Given statement:
Cost of cherries is $1 more per container than blueberries.
Cost of blueberries is $1 more per container than strawberries.
The product of all 3 prices is 5 times the total cost.
One container of each has been purchased.
Explanation:
Check the value of x where the graph intersects the x -axis.
From the graph, the graph is intersecting the x -axis at
Therefore,
Hence, Cost of strawberries per container is $3.
Cost of blueberries per container is
Cost of cherries per container is
Chapter 5 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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