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) = –x2 + 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)