Arianna kicks a soccer ball off the ground and into the air with an initial velocity of 42 feet per second. Assume the starting height of the ball is 0 feet. Approximately, how long does it take until the soccer ball hits the ground again? 1.3 secs 2.6 secs 16.0 secs 27.6 secsQuestion 2 (Multiple Choice Worth 1 points)Ken is building a table. He attached planks of wood and now wants to build a border around the planks. The area of the entire table should be no larger than 3,276 square inches. All together, the planks are 36 inches wide and 72 inches long. Which quadratic equation represents the area of the planks and border combined? (The border must have equal width on each side.) 4x2 + 216x + 2,592 = 0 4x2 + 216x − 684 = 0 2x2 + 216x − 3,276 = 0 x2 + 108x + 3,276 = 0Question 3 (Multiple Choice Worth 1 points)A particle is moving along a projectile path where the initial height is 96 feet with an initial speed of 16 feet per second. What is the maximum height of the particle? 100 feet 96 feet 60 feet 56 feetQuestion 4 (Multiple Choice Worth 1 points)Jules kicks a soccer ball off the ground and into the air with an initial velocity of 25 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach? 0.8 ft 1.6 ft 9.8 ft 19.6 ftQuestion 5 (Multiple Choice Worth 1 points)A juggler is performing an act by juggling several balls. The juggler throws the balls up at an initial height of 3.9 feet with a speed of 14.8 feet per second. If the juggler did not catch a ball, about how long will it take the ball to hit the floor? 1.45 secs 1.14 secs 0.28 secs 0.21 secsQuestion 6 (Multiple Choice Worth 1 points)A golf ball is hit from the ground with an initial velocity of 208 feet per second. Assume the starting height of the ball is 0 feet. How long will it take the golf ball to hit the ground? 13 secs 21 secs 42 secs 6 secsQuestion 7 (Essay Worth 4 points)Use complete sentences to explain how you would use graphing technology to find the solutions of 0 = −x2 + 2.5x + 1. What do the solutions of 0 = −x2 + 2.5x + 1 represent on the graph of the equation?

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The ball problems are super easy when they’re multiple choice. The height is given by y = 16t², so let’s plug in some simple values for t: If t=1 second, that’s 16 feet. 2s gives 64′. Here’s a table:t:y1: 162: 643: 144From this, we can guess a few in-between values:0.5: ≈51.5: ≈402.5: ≈100Next, we need to be able to convert speeds into times. That’s easy because v=32t. So when t is 1 second, v is 32 feet per second, and so on.t: v1: 322: 643: 96and0.5: ≈81.5: ≈502.5: ≈80Now watch closely because this will save you on a multiple-choice test:For the Arianna problem, the speed has to go from 42ft/s to zero, and then back to 42 because it will land at the same speed it started with. From our t’v table, we see that this takes about 1.5s, but it has to do it twice, so about 3s. The answer is 2.6.For the particle problem, our t’v table says 16ft/s means about 3/4 of a second. Then our t’y table says 3/4s is about 8 feet. It started at 96 feet according to the problem, so the answer is about 100.For the Jules problem, 25ft/s is a little less than 1s, which is a bit under 16 feet upward. The answer must be 9.8ft.For the juggler problem, it’s tricky: 14.8ft/s means a little less than 3/4s, but this is only the upward time. The fall will be a bit longer, so we are looking at somewhere around a second and a half: 1.45s.For the golf ball, 208ft on our t’y table is maybe 3.5 or 4s. Again, this is only half the trip. 6s.