Concept explainers
a.
To find: The moisture content that maximizes the popping volume for hot-air popping and find the maximum volume.
The moisture content
Given information:
The equation of popping volume for hot-air popping is
Concept used:
The x-coordinate of the vertex of a quadratic function of the form
The vertex of the quadratic function represents the maximum/minimum point of the function.
If
Calculation:
For the given function
Then,
Therefore, the moisture content
Now, substitute
Therefore, the maximum popping volume is
Conclusion:
The moisture content
b.
To find: The moisture content that maximizes the popping volume for hot-oil popping and find the maximum volume.
The moisture content
Given information:
The equation of popping volume for hot-oil popping is
Concept used:
The x-coordinate of the vertex of a quadratic function of the form
The vertex of the quadratic function represents the maximum/minimum point of the function.
If
Calculation:
For the given function
Then,
Therefore, the moisture content
Now, substitute
Therefore, the maximum popping volume is
Conclusion:
The moisture content
c.
To graph: Graph the functions on the same coordinate plane and find the domain and range of each function.
The domain of the function
The domain of the function
Given information:
The equation of popping volume for hot-oil popping is
Concept used:
The x-intercept of the function of the form
The vertex of the quadratic function represents the maximum/minimum point of the function.
If
Graph:
Use a graphing calculator to graph the functions on the same coordinate plane.
Calculation:
The x-intercept of the function
Since volume cannot be negative, the graph only exists for non-negative y-values. That means, the graph exists between the x-intercepts of the function.
So, the domain of the function
The minimum value of the function on its domain is 0 and the maximum value is 55.5. So, the range of the function is
Similarly, the domain of the function
Conclusion:
The domain of the function
The domain of the function
Chapter 1 Solutions
EBK ALGEBRA 2
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