Question

Question 1 - 20 marks This question is based on your work on MỤ123 up to and including Unit 10. Katie likes to play volleyball. When she serves, the trajectory of the ball after she hits it can be modelled by the quadratic equation 295 where y represents the height in metres of the ball above the ground, and x represents the horizontal distance in metres of the ball from the position where it was struck by Katie. Assume that the surface of the volleyball court is horizontal 9 5 (a) The graph of y-+ +is a parabola. (i) Is the parabola u-shaped or n-shaped? How can you tell this from the equation? (ii) Use algebra to find the r-intercepts (iii) Explain why the y-intercept is (iv) Find the equation of the axis of symmetry, explaining your method Use this information to find the coordinates of the vertex, rounding your answers where necessary to one decimal place Provide a sketch of the graph of the parabola, either by hand or by using Graphplotter. You should refer to the graph-sketching strategy box in Section 2.4 of Unit 10 for information on how to sketch and label a graph correctly (v) (b) In this part of the question, you are asked to consider the trajectory of 2 9x 5 -+-+-in the volleyball modelled by the equationy- - conjunction with the results that you found in part (a). (i) Find the height of the ball when it is 3 metres horizontally from the position where Katie serves it. (ii) Use your answer to part (a)(iv) to find the maximum height reached by the volleyball (ii) What does the y-intercept represent in the context of this model?[] (iv) Assuming that the ball is not returned or touched in the air, how far is it horizontally from where Katie served it when it first lands on the court? Explain your answer. 12]

Answer 1

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