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Concept explainers
(a)
The sprinkler that send the water at the farthest.
(a)
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Answer to Problem 26PPS
The parabola for Sprinkler C is the most compressed vertically, so it will send water the farthest.
Explanation of Solution
Given information:
The path of water from a sprinkler can be modelled by quadratic functions. The following functions model paths for three different sprinklers.
Formula used:
The quadratic functions are of the form f (x) = ax2 + c
Calculation:
All three of the quadratic functions are of the form f (x) = ax2 + c. Use a graphing calculator to compare the graphs of the three functions. All three of the quadratic functions are of the form f (x) = ax2+ c. Use a graphing calculator to compare the graphs of the three functions.
The value of a in the function for Sprinkler C is the smallest of the three. Therefore, the parabola for Sprinkler C is the most compressed vertically, so it will send water the farthest.
Conclusion:
The parabola for Sprinkler C is the most compressed vertically, so it will send water the farthest.
(b)
The sprinkler that send the water at the highest.
(b)
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Answer to Problem 26PPS
The parabola for Sprinkler A is translated up the most, so it will send water the highest.
Explanation of Solution
Given information:
SPRINKLERS the path of water from a sprinkler can be modelled by quadratic functions. The following functions model paths for three different sprinklers.
Formula used:
The quadratic functions are of the form f (x) = ax2 + c
Calculation:
All three of the quadratic functions are of the form f (x) = ax2 + c. Use a graphing calculator to compare the graphs of the three functions. All three of the quadratic functions are of the form f (x) = ax2+ c. Use a graphing calculator to compare the graphs of the three functions.
The value of c in the function for Sprinkler A is the largest of the three. Therefore, the parabola for Sprinkler A is translated up the most, so it will send water the highest.
Conclusion:
The parabola for Sprinkler A is translated up the most, so it will send water the highest.
(c)
The sprinkler that send the water at the narrowest path.
(c)
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Answer to Problem 26PPS
The parabola for Sprinkler A is the most stretched vertically, so it will expand the least, and therefore have the narrowest path.
Explanation of Solution
Given information:
SPRINKLERS the path of water from a sprinkler can be modelled by quadratic functions. The following functions model paths for three different sprinklers.
Formula used:
The quadratic functions are of the form f (x) = ax2 + c
Calculation:
All three of the quadratic functions are of the form f (x) = ax2 + c. Use a graphing calculator to compare the graphs of the three functions. All three of the quadratic functions are of the form f (x) = ax2+ c. Use a graphing calculator to compare the graphs of the three functions.
The value of a in the function for Sprinkler A is the largest of the three. Therefore, the parabola for Sprinkler A is the most stretched vertically, so it will expand the least, and therefore have the narrowest path.
Conclusion:
The parabola for Sprinkler A is the most stretched vertically, so it will expand the least, and therefore have the narrowest path.
Chapter 9 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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