SOLUTION: Q1
a) Orla and Maeve like to play volleyball once a week. When Maeve serves, the tractory of the ball aftre she hits it can be modelled by the quadratic equation
y=-1/8x^2+
a) Orla and Maeve like to play volleyball once a week. When Maeve serves, the tractory of the ball aftre she hits it can be modelled by the quadratic equation
y=-1/8x^2+9/8x+5/4
where y reprsents the height in metres of the ball above the ground , and x reprsents the horizontal distnace of the ball from the position where it was struck by Maeve , measured in metres. Assume that the surface of the volleyball court is horizontal
a) the graph of y=-1/8x^2+9/8x+5/4 is a parabola
(i) is the parabola a u-shaped or a n-shaped? How can you tell this from the equation?
(ii)Use algebra to find the x-intercepts and y-intercepts
(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 parabola
Q1 (b)in this part of the question you are asked to consider the trajectory of the ball modelled by the equation y=-1/8x^2+9/8x+5/4, in the conjunction with the results that you found in part (a)
(i) Find the length of the ball when it is 4 metres horizontally from the postion where Maeve 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 when Maeve served itwhen it first lands on the court/ Explain your answer
Q2 A) use the quadratic formula to solve the equation 3p^2+5p-11=0
give your answers to two decimal places
b) this part of the question concerns the the quadratic equation 7x^2-3x-11=0
(i)Find the discriminant of the quadratic expression 7x^2-3x-11
(ii) What does this tell you about the number of solutions of the equation ? explain your answer breifly
(iii) what does this tell you about the graph of y=7x^2-3x-11
