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
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
(i)Is the parabola u-shaped or
n-shaped? How can you tell this from
(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