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2 m 4 m 6 m 20 m 14 m The diagram to the right shows a thief as he leaps from the roof of one building to the roof of another in an attempt to escape capture.

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Presentation on theme: "2 m 4 m 6 m 20 m 14 m The diagram to the right shows a thief as he leaps from the roof of one building to the roof of another in an attempt to escape capture."— Presentation transcript:

1 2 m 4 m 6 m 20 m 14 m The diagram to the right shows a thief as he leaps from the roof of one building to the roof of another in an attempt to escape capture. As he jumps from the edge of the building, his leap takes a parabolic path. He jumps from a 20 meter building and reaches a maximum height 3 meters above the roof. The roof of the building that he jumps to is 14 meters high. How far must he jump horizontally to make it?

2 When a baseball player hits a baseball, the ball travels in a parabolic trajectory. At the same time he loses his grip on the bat which also takes a parabolic trajectory. The equations for each are defined by the following functions where x represents the horizontal distance and the function represents the height. Ball:Bat: Which travels further horizontally: the ball or the bat?

3 A bird takes off from a tree and flies in a straight line that crosses through the trajectory of the ball at 2 points. At what height was the bird when he took off from the tree? A golfer strikes his golf ball and watches it travel through its parabolic trajectory defined by the equation: g(x) = -(x – 7) x – horizontal distance g(x) – height x 9 m y 4 m

4 20 m 2 m 4 m 6 m 14 m y = a(x – h) 2 + k Vertex: (6,23) Other point: (4,20) y = a(x – 6) = a(4 – 6) = 4a a = 20 – 23 4a = -3 a = y = -0.75(x – 6) = -0.75(x 2 – 12x + 36) = -0.75x 2 + 9x – – 14 0 = -0.75x 2 + 9x – 18 0 = x 2 – 12x + 24 x 1 = 2.54 mx 2 = 9.46 m 9.46 m The value of 2.54 m must be disqualified because we are looking for a value beyond 4 m (the point he jumped from) – 4 = 5.46 m He must jump 5.46 meters to get to the other building.

5 When a baseball player hits a baseball, the ball travels in a parabolic trajectory. At the same time he loses his grip on the bat which also takes a parabolic trajectory. The equations for each are defined by the following functions where x represents the horizontal distance and the function represents the height. Ball:Bat: Which travels further horizontally: the ball or the bat? The ball travels a distance of 8 meters whereas the bat travels a distance of 10 meters.

6 A bird takes off from a tree and flies in a straight line that crosses through the trajectory of the ball at 2 points. At what height was the bird when he took off from the tree? A golfer strikes his golf ball and watches it travel through its parabolic trajectory defined by the equation: g(x) = -(x – 7) x – horizontal distance g(x) – height x 9 m y 4 m g(4) = -(4 – 7) = -(-3) = = 7 (4,7) g(9) = -(9– 7) = -(2) = = 12 (9,12) The points (4,7) and (9,12) are points on the parabola but they are also points on the straight line. y – 7 = x – 4 y = x – y = x + 3 The tree is at x = 0. y = x + 3 y = y = 3 The bird is at a height of 3 meters when it takes off from the tree.

7 A buyer is given a 3 payment options when he is shopping for a car as shown by the following graph. The horizontal axis represents the number of months for the payment plan while the vertical axis represents the amount paid Amount paid in $ Number of months OPTION A OPTION B OPTION C What are the down payments for each option? What are the monthly payments for each option? Which option is cheapest overall? After how many monthly payments is the amount paid the same for: Option A and Option B? Option B and Option C? Option A and Option C?

8 A buyer is given a 3 payment options when he is shopping for a car as shown by the following graph. The horizontal axis represents the number of months for the payment plan while the vertical axis represents the amount paid Amount paid in $ Number of months OPTION A OPTION B OPTION C What are the down payments for each option? What are the monthly payments for each option? Which option is cheapest overall? After how many monthly payments is the amount paid the same for: Option A and Option B? Option B and Option C? Option A and Option C? A: $12000; B: $5000; C: $0 A: $0/mo; B: $250/mo; C: $500/mo A: $12000; B: $14000; C: $18000 A is cheapest. After how many monthly payments is the amount paid the same for: Option A and Option B? 30 months Option B and Option C? 20 months Option A and Option C? 24 months

9 Given the following linear equation, determine the equation of the parabola that the line intersects in 2 places. The line intersects the parabola at its maximum 6 units from the y-axis and it intersects the parabola also 10 to the right of the y-axis. 10 units 6 units

10 Given the following linear equation (f(x)), determine the equation of the parabola that the straight line intersects in 2 places. The line intersects the parabola at its maximum 6 units from the y-axis and it intersects the parabola also 10 to the right of the y-axis. 10 units 6 units The points (6,9) and (10,3) are on the line but they are also on the parabola. In fact, the point (6,9) is the vertex (h,k) of the parabola.

11 A rope ties a sailboat to a pier. The rope hangs in the shape of a parabola and at its lowest point is just one-quarter of a meter above the water. The sailboat is 18 meters from the pier. The rope is closest to the water 12 meters from the pier. The bow of the boat is 1.25 meters above the water. How high is the top of the pier above the water? 18 meters 12 meters x y

12 A rope ties a sailboat to a pier. The rope hangs in the shape of a parabola and at its lowest point is just one-quarter of a meter above the water. The sailboat is 18 meters from the pier. The rope is closest to the water 12 meters from the pier. The bow of the boat is 1.25 meters above the water. How high is the top of the pier above the water? 18 meters 12 meters x y (-12, 0.25) (-18, 1.25) The pier is at the y-axis and therefore its height above the water is the y-intercept. To find this, let x = 0. Pier is 4.25 meters above the water.


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