You should be able to answer this question after studying Unit 2. (a) (i) Write the following quadratic expression 31 - 12r + 8 in completed square form. (ii) Hence solve the equation 3r- - 12r + 8= 0. (iii) Using the Strategy described in Section 4.9 of Unit 2 in Book A, or any well-described method, sketch the graph of y = 3x - 12r + 8. (You should sketch this by hand rather than using any software.) (b) A contestant in the shot put event at a local athletic competion throws their shot. The trajectory of the shot can be modelled by the equation 7= 1.8 + 6: - 0.512, where r is the horizontal displacement (in metres) of the shot from the contestant and y is the vertical displacement (in metres) measured from the ground. You may assume that all ground in the shot put field is level and the contestant throws the shot forwards. (i) What is the exact maximum height of the shot above the ground. given that this occurs when the horizontal displacement of the shot from the contestant is 6 metres? (ii) What is the distance of the throw, i.e. the distance from the contestant to where the shot lands? Give your solution to one decimal place