quadratic equation

Question Description

Hi, Please help me with my practice test. Thank you in advance for any help.

Susan and Linda like to play volleyball once a week. When Linda serves, the trajectory of the ball after she hits it can be modelled by the quadratic equation  y = -1/8x2 + 9/8x +5/4  

where y represents the height in metres of the ball above the ground, and x represents the horizontal distance of the ball from the position where it was struck by Linda, measured in metres. Assume that the surface of the volleyball court is horizontal.

(a) The graph of y = -1/8x2 + 9/8x +5/4  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 x-intercepts and y-intercept. 

(iii)  Find the equation of the axis of symmetry, explaining your method. Use this information to find the coordinates of the

vertex, giving your answers to one decimal place. 

(iv)  Provide a sketch of the graph of the parabola.


(b) In this part of the question, you are asked to consider the trajectory of the ball modelled by the equation y = -1/8x2 + 9/8x +5/4  , in

conjunction with the results that you found in part (a).

(i)  Find the height of the ball when it is 4 metres horizontally from

the position where Linda serves it. 

(ii)  Use your answer to part (a)(iii) to find the maximum height

reached by the ball. 

(iii)  What does the y-intercept represent in the context of this model? 

(iv)  Assuming that the ball is not returned, how far will it be horizontally from where Linda served it when it first lands on the

court? Explain your answer.

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Final Answer

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Duke University

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