The function h = f(t) = 8t^2 + 80t + 8 expresses the height of a rock, measured in feet, in terms of the number of seconds since it was launched straight up on the planet Krypton. End your explanations to questions (c)-(g) below with a concluding sentence that both captures and answers the question. Do not use the quadratic formula. (a) Rewrite the above function in standard form. (b) Find the correct domain for the function f. Then graph the function over this domain. (c) Find the maximum height of the rock. (d) When is the rock the same height as it is 3 seconds after being launched? (e) When is the rock the same height as it is 1.732 seconds after being launched? Use the graph to answer this question. (f ) When is the rock 50 feet lower than it is 2 seconds after being launched? (g) Find a three-second interval during which the rock falls at an average rate of 20 ft/sec.