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Created with Fabric.js 1.4.5 VHEMES vhemes = visual + themesstart by dragging a predesigned vheme onto the canvas OBJECTS drag and drop icons,shapes, text or upload your own from our extensive library of artwork your artboard start from scratch[clears the canvas] PAPER FOOTBALL PARABOLAby Tommy MacLeodMy freakishly mathematical parents were watching me play a game of paper football and wondered about a formula to describe the arc of the paper football when it was flicked on a kickoff and on a field goal punt. They noticed that I was fairly consistent and so they were able to determine that the formula y = -2x2 + 16x + 33 was a reasonable model for the path the football took, where x is the horizontal distance the ball travels and y is the balls height above the ground.a. What is the y-intercept of this parabola and interpret its meaning for this problem? The table I was playing on was 33 inches tall and 8 feet long. I start at the edge of the table so the distance is 0 ft with a height of 33 in, making it the y-intercept of the parabola (0, 33).b. What is the maximum height the paper football reaches? At what distance does this occur?It reaches its peak at the vertex (4, 65), meaning that it is halfway down the table at 4 feet and it is 65 inches from the ground or 32 inches above the table. c. At what point on the table will the paper football touch down again?The paper football comes down to table height (33 in) again at 8 feet, right at the end of the table (8, 33).d. If the paper football hits the ground, how far will it be from the end of the table? If no one is there to block it and it goes to the floor (height of 0), it lands 9.7 feet from where it started or 1.7 feet from the end of the table. That is one of the x-intercepts of the parabola (9.7,0). (The other x-intercept at (-1.7, 0) is irrelevant in this setting.)e. On a field goal punt, if my opponent sets his goal posts 0.5 ft from the end of the table, how far above the table should s/he hold his hands in order to block my punt? If he holds his hands 0.5 ft from the end of the table, that is 7.5 ft from my end. If x = 7.5, y = 40.5, or 40.5 inches above the ground, which is 7.5 inches above the table. TEXT
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