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Consider the following function. F(x) = x2 - 4x Use a graphing utility to graph the quadratic function. Find the x-intercept(s) of the graph and compare them with the solutions of the corresponding quadratic equation when f(x) = 0. smaller x-value (x, F(x) ) = larger x-value (x, f(x)) =Find two quadratic functions, one that opens upward and one that opens downward, whose graphs have the given x-intercepts. (There are many correct answers.) (-4, 0), (4, 0) opens upward F(x) = opens downward g(x) =The path of a diver is modeled by F(x) = - 24 * + 11, 9 where f(x) is the height (in feet) and x is the horizontal distance (in feet) from the end of the diving board. What is the maximum height (in ft) of the diver? ftThe path of a pumpkin launched from a compressed air cannon is modeled by f(x) = -. 3 '+ _x + 25, where f(x) is the height (in feet) and x is the horizontal distance (in feet) from where the pumpkin was launched. 10,000 (a) How high (in ft) is the pumpkin when it is launched? ft (b) What is the maximum height (in ft) of the pumpkin? ft (c) The world record distance for a launched pumpkin is 5,545 feet. Does this launch break the record? O Yes. This launch breaks the record. O No. This launch does not break the record.A manufacturer of lighting fixtures has daily production costs of C = 800 - 10x + 0.25x", where C is the total cost (in dollars) and x is the number of units produced. What daily production number yields a minimum cost? fixtures