CULMINATING ACTIVITY -PART 1 Strands 1 and 2 NAME: DATE: 1. The motion of a ball, whether thrown or kicked, follows a parabolic path. Your enthusiastic clay was watching a football cune one Friday afternoon. As usual, your math teacher was busy analyzing a field goal kick and noticed that the kicker was 3 matters from the uprights (goal posts), Knowing that the crossbar was 3 meters above the ground, it was estimated that the football sailed through the goal posts at a whopping 2 meters above the ground. Here's a picture you can visualize: a) Assuming that the vertex of the path occurs when it crosses the posts (that is, it travels another 3 meters after the posts). sketch the path of the ball in the grid below. HINTS: Place points down for the vertex and the zeroes first. Then work on the step pattern. The &-axis represents the ground. The ball is kicked at (9,0). height (meters) distance along ground (meters)b) Using the vertex equation below from that represents the parabola from this problem, Convert it to standard form: HINT: Expand and collect like terms y= -(x-3):+9 What are the zeroes (x intercepts) of the parabola and what do they represent in the scenario? dj How high is the ball when it is 2 meters from the kicker? When the ball is 5 meters high, how far is it from the kicker? HINT: Use your graph to help you The crossbar is 3 meters above the ground. If the kicker is 1 meter from the goal posts, will the field kick be good (that is, will it make it over the crossbar)? [1 mark] FLINT: Use the graph you sketched. The goal posts were originally 3 meters from the kicker. cross barMBF 30 - Culminating Part 1 Page 3 of 4 2. After much deliberation, it was decided that the football team needed new jerseys made of 1009% heavyweight nylon whup knit and 100%% tricot mesh. These new jerseys will debut during the next school your. The new jerseys will cost $35.00 each a) If there are 30 football players on the team, how much will the total cost be? b) To raise money for the new jerseys, the team held a fundraising car wash. In total, they raised $1000 a Little short of their goal. so to speak. They decided to invest the money into a bank hecount that pays interest for 6 months, At the bank, they were told there are two options: OPTION 1 OPTION An kcount which pays 890 per amman An recount which pays 12ve per annum compounded monthly. Using calculations, show which account will carn the money needed for the jerseys. (6 marks] OPTION 1 OPTION 2 A - P(1 + iF 1 = Pn A= P+1 Conclusion: c) Describe the difference between simple interest and compound Interest. (ie. how it is calculated, formulas used, type of growth shape of graph)MBF 3C - Culminating Part 1 Page 4 of 4 3. After the new jerseys were introduced, attendance at each paine lacreased according to the equation y - 25(1.5)' ") To represent the trend in attendance, complete the table of values, and graph the points on the and below. by y = 25(1.5)" 0 2 Number of people Number of games b) What type of growth does this graph represent? [ie. linear, quadratic or exponential] c) Is this function increasing or decreasing? d) How can you tell this function is increasing or decreasing just by looking at the equation. NEXT, GO COMPLETE PART 2