Honors Quadratic Functions Shopping Mall Activity (30 points total) Directions: Answer all questions in complete sentences...

 

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Honors Quadratic Functions Shopping Mall Activity (30 points total) Directions: Answer all questions in complete sentences and show all work to receive full credit. As a commercial developer, you have planned to build a new shopping mall. The financial analyst hired for the project determines that the profit function for the total profit earned in thousands of dollars, S(x), from the shopping mall is S(x) = x + 36x- 288, where x represents the number of retail stores. 1. Graph the profit function of the shopping mall, S(x), and label the following key features: a. y-intercept (1 point) b. x-intercepts (2 points) c. interval(s) where the function is increasing (1 points) d. interval(s) where the function is decreasing (1 point) e. interval(s) where the function is positive (1 point) f. interval(s) where the function is negative (1 point) g. vertex (1 point) h. axis of symmetry (1 point) 2. Determine the domain and range of the profit function, S(x), and interpret their meaning in the context of the problem (6 points) 3. Determine the number of retail stores the shopping mall should have that will guarantee the shopping mall will not lose money. Show mathematically how this can be calculated. (8 points) 4. What is the optimal number of retail stores the shopping mall should have to maximize profit? What will the profit be at that point (in thousands of dollars)? Find these values using the necessary mathematical calculations and show all necessary work. (7 points) Honors Quadratic Functions Shopping Mall Activity (30 points total) Directions: Answer all questions in complete sentences and show all work to receive full credit. As a commercial developer, you have planned to build a new shopping mall. The financial analyst hired for the project determines that the profit function for the total profit earned in thousands of dollars, S(x), from the shopping mall is S(x) = x + 36x- 288, where x represents the number of retail stores. 1. Graph the profit function of the shopping mall, S(x), and label the following key features: a. y-intercept (1 point) b. x-intercepts (2 points) c. interval(s) where the function is increasing (1 points) d. interval(s) where the function is decreasing (1 point) e. interval(s) where the function is positive (1 point) f. interval(s) where the function is negative (1 point) g. vertex (1 point) h. axis of symmetry (1 point) 2. Determine the domain and range of the profit function, S(x), and interpret their meaning in the context of the problem (6 points) 3. Determine the number of retail stores the shopping mall should have that will guarantee the shopping mall will not lose money. Show mathematically how this can be calculated. (8 points) 4. What is the optimal number of retail stores the shopping mall should have to maximize profit? What will the profit be at that point (in thousands of dollars)? Find these values using the necessary mathematical calculations and show all necessary work. (7 points)