Chapter 9.2, Problem 26PPS

(a)

To determine

The sprinkler that send the water at the farthest.

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.

  $\text{Sprinkler}\text{A:}y=-0.35x^2+3.5$

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)

To determine

The sprinkler that send the water at the highest.

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.

  $\text{Sprinkler}B\text{:}y=-0.21x^2+1.7$

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)

To determine

The sprinkler that send the water at the narrowest path.

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.

  $\text{Sprinkler}C\text{:}y=-0.08x^2+2.4$

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.