Modeling with quadratic functions Student Activity Sheet 5; use with Exploring Using y = ax 2 + bx + c to model data

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Justin Holt
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1 1 What relationship is being compared when discussing Pete s shot? Horizontal distance in feet, x Height in feet, y Use a graphing calculator to make a scatterplot of Pete s data What type of shape might the points be creating? What type of function creates this type of shape? 3 Use your graphing calculator to find a quadratic function rule that fits the data 4 Now add the graph of this rule to the scatter plot on your graphing calculator Page 1 of 5

2 Pete s shot can be modeled by the function y = -002x x + 65 Use the quadratic rule for Pete s data to complete the following puzzle 65 y y x 3462 all real numbers 0 x 15 all real numbers about The domain for the function rule is 6 The range for the function rule is 7 The values of the domain that make sense for this situation are 8 The values of the range that make sense for this situation are Pete s shot can be modeled by the function y = -002x x + 65 Use the quadratic rule for Pete s data to complete the following puzzle (104, 14) x = 0 15 the minimum height of the ball (14, 104) x = the maximum height of the ball 9 Pete releases the ball at a height of 65 feet If the ball misses the basket and continues its path to the floor without being interrupted, it will travel a total of about feet horizontally 10 The coordinates of the vertex of the parabola are approximately 11 The axis of symmetry for the parabola is approximately Page 2 of 5

3 12 When x = 0, where is the ball on Brian and Jerry s graph? 13 When x = 0, where is the ball on Pete s graph? 14 In order to shift Brian s graph, such that his release point is at x = 0, he has to change his equation from y = -2x to (His release point is about 191 feet from the peak of his shot) 15 In order to shift Jerry s graph, such that his release point is at x = 0, he has to change his equation from y = -x to (His release point is about 298 feet from the peak of his shot) Page 3 of 5

4 16 REINFORCE A biologist was interested in the number of insect larvae present in water samples as the temperature of the water varied He collected the following data: Temperature (C ) Insect Population a Make a scatterplot of the data Given that the value of b is 75, experiment with values for a and c in y = ax 2 + bx + c to fit a quadratic function to your plot b Write a verbal description of what the graph tells you about the insect population and the temperature of the water samples c When is the insect population greatest? Page 4 of 5

5 17 REINFORCE A punter on a football team kicks a football upward from the ground with an initial velocity of 63 feet per second The height of the football stadium is 70 feet The height of an object with respect to time is modeled by the equation h = 1 2 gt2 + vt + s where g is -32 ft/sec 2, v is the initial velocity, and s is the initial height a Write a function that models this situation b Sketch and describe the graph of this function c At what times will the football be the same height as the top of the stadium? Explain your answer d Suppose the punter s initial velocity is 68 feet per second At what times will the football be the same height as the top of the stadium? Justify your answer Page 5 of 5

The coordinates of the vertex of the corresponding parabola are p, q. If a > 0, the parabola opens upward. If a < 0, the parabola opens downward.

The coordinates of the vertex of the corresponding parabola are p, q. If a > 0, the parabola opens upward. If a < 0, the parabola opens downward. Mathematics 10 Page 1 of 8 Quadratic Relations in Vertex Form The expression y ax p q defines a quadratic relation in form. The coordinates of the of the corresponding parabola are p, q. If a > 0, the