Suppose f(m) = 9:2 3:1: 28. a. Write f(w) = $2 3w 28 in factored form. f0\") = I Preview Syntax error Enter an al_ebraic ex u ression [more..] b. Determine the root(s) for f. If there is more than one, write them as a comma-separated list. Need a hint? a: = a Preview c. What z-value produces a maximum (or minimum) value for f (3:)? Need a hint? m = a Preview d. What is the maximum (or minimum) value of f (it)? Need a hint? y = a Preview e. What is the location of the function's vertex? Need a hint? (w, y) = a Preview f. The yvalue of the vertex represents the function's maximum v a value. Need a hint? An ice cream shop nds that its weekly prot P (in dollars) as a function of the price w (in dollars) it charges per ice cream cone is given by the function 9, dened by g(a:) = 120922 + 10002: 140. a. What price should the store charge to maximize their prot? Need a hint? $ a Preview b. According to the model, what is the store's maximum weekly prot? Need a hint? $ a Preview c. What prices would cause the weekly prot to be $0? (Write your answers as a comma-separated list.) Need a hint? $ a Preview (1. Another ice cream shop developed a similar model for their weekly prot. Its model is f where x) = 9(a) + 400. What does this tell us? Select all that apply. The two stores have different maximum weekly prots. [:1 To maximize weekly prots, both stores should charge the same price per cone. When this shop charges the same price per ice cream cone, it will always earn $400 dollars per week less than the original store. When this shop charges the same price per ice cream cone, it will always earn an additional $400 dollars per week compared to the original store. A quadratic function f has roots of x = - 1 and x = 5 and it contains the point (6, 28). Write the function's formula. a. In order to complete this task, we first must recognize that we can always write a quadratic function in a form f(t) = a . (x - x1)(x - x2) where x1 and x2 are the roots. Therefore, we begin by writing f(x) = a(x - ( -1)) (x - 5), or f(x) = a(x + 1)(x -5). b. Next, we need to find the correct value of a. So we enter the ordered pair we know, in this case (x, y) = (6, 28). f(a) = a(2 + 1) (2 -5) 28 = a(6 + 1)(6 -5) c. To complete the process, simplify the expressions above and solve for a. The value of a that makes the statement true is a = Preview d. Replace the value of a in the answer from part (a) to define the formula. f(ac) = Preview e. Rewrite the function in standard form (the form f(x) = ax" + ba + c). f(a) = PreviewA rock is thrown upward from a bridge that is 73 feet above a road. The rock reaches its maximum height above the road 0.65 seconds after it is thrown and contacts the road 3.63 seconds after it was thrown. Write a function f that determines the rock's height above the road (in feet) in terms of the number of seconds t since the rock was thrown. t) = |:] Preview Hint: the function f can be written in the form f(t) = c - (t t1)(t t2) for xed numbers c, 251, and t2