1. on the earth's moon, gravity is only one-sixth as. strong as it is on earth, so an object on the moon will fall one-sixth the distance it would fall on earth in the same time. this means that the gravity distance function for a falling object on the moon is s = 16 \ 2 8 2 - t ors = -t . where ¿/represents time since the object is released, in seconds, and s is the distance fallen, in ft. 406 chapter 4 problem solving with quadratic and variation function models a. how far does an object on the moon fall in three seconds? b. how long does it take an object on the moon to fall 96 feet? c. graph the moon's gravity function on a properly scaled and labeled coordinate axis in or on a graphing calculator for t — 0 to t = 5. d. use the graph to estimate how long it takes an object on the moon to fall 35 feet. e. write an equation to determine the required time in part d. solve the equation algebraically. f. how does your answer in part e compare to your estimate in part d? 2. a. the graphs of y = x2 , y = -x2 and y = 5x2 appear in the following graphing calculator screen. match the equation with the graph. activity 4.1 the amazing property of gravity 407 b. is the graph of y — 0.75.x2 wider or narrower than the graph of y = 10.x2 ? verify using a graphing calculator. • c. is the graph of y = 10.x wider or narrower than the graph of y = 5x ? 3. solve the following equations: a. 5xl = 45 b. 9x2 = 0 ; . c. -25x2 = 100 d. x2 = 5 e. 2x2 = 20 f. f = 32 2 _ „. 4. solve the following by first writing the equation in the form x¿ = c: a. x2 - 49 = 0 b. 15 + cl = 96 c. 3a2 - 21 = 27 ig in a right triangle, as shown in the following diagram, the side c opposite the right angle is called the hypotenuse, and the other two sides a and b are called legs. the pythagorean theorem states that in any right triangle, the lengths of the three sides are related by the equation c2 = a2 + b2 . - y 408 chapter 4 problem solving with quadratic and variation function models use the pythagorean theorem to answer exercises 5-6. ts « *+ b a 5. determine the length of the hypotenuse in a right triangle with legs 5 inches and 12 inches. 6. one leg of a right triangle measures 8 inches and the hypotenuse 17 inches. determine the length of the other leg.