Concept explainers
(a)
Find which sprinkler will send water the farthest.
(a)
Answer to Problem 30PPS
The parabola for Sprinkler C is the most compressed vertically, so it will send water the farthest.
Explanation of Solution
Given:
The path of water from sprinkler can be modeled by quadratic functions. The following functions model paths for 3 different sprinklers .
Concept Used:
Al three of the quadratic functions are of the form
The value of a in the function for sprinkler C is a smallest of the three.
Therefore, the parabola for Sprinkler C is the most compressed vertically, so it will send water the farthest.
Thus, the parabola for Sprinkler C is the most compressed vertically, so it will send water the farthest.
(b)
Find which sprinkler will send water the highest.
(b)
Answer to Problem 30PPS
The parabola for sprinkler A is translated up the most, so it will send water the highest.
Explanation of Solution
Given:
The path of water from sprinkler can be modeled by quadratic functions. The following functions model paths for 3 different sprinklers.
Concept Used:
Al three of the quadratic functions are of the form
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.
Thus, the parabola for sprinkler A is translated up the most, so it will send water the highest.
(c)
Find which sprinkler will produce the narrowest path.
(c)
Answer to Problem 30PPS
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:
The path of water from sprinkler can be modeled by quadratic functions. The following functions model paths for 3 different sprinklers.
Concept Used:
Al three of the quadratic functions are of the form
When comparing with
The value of a in the function of 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.
Thus, 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
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