Question 1 20 marks This question is based on your work on MU123 up to and including Unit 10. (a) This part of the question concerns the quadratic equation 3x- - 17x - 12 - 0. (i) Find the discriminant of the quadratic expression 327 - 17x - 12. (ii) What does this discriminant tell you about the number of solutions of the equation? Explain your answer briefly. (iii) What does this discriminant tell you about the graph of 1 -3x- - 171 - 12? (b) Figure 1 shows part of the graph of the quadratic function # - -1 +72+18. (-2.0) (9.0) Figure 1 (i) Explain why the graph of the quadratic function y - -+ +7x + 18 is n-shaped. (ii) Write down the y-intercept. (iii) Find the equation of the axis of symmetry of the parabola given by y - -r +72 + 18, explaining your method. (iv) Use your answer to part (b) (iii) to find the coordinates of the vertex of the parabola given by y - -+ + 7x + 18.(c) This part of the question concerns the quadratic function y = r' + 18x + 42. (i) Write the quadratic expression r' + 18x + 42 in completed-square form. (ii) Use the completed-square form from part (c)(i) to solve the equation r' + 18x +42 = 0, leaving your answer in exact (surd) form. (iii) Use the completed-square form from part (c) (i) to write down the coordinates of the vertex of the parabola y = x2 + 18 + 42. (iv) Provide a sketch of the graph of the parabola y = x2 +18r +42, either by hand or by using a suitable graphing software package like Graphplotter. If you intend to go on to study more mathematics, then you are advised to sketch the graph by hand for the practice. Whichever method you choose, you should refer to the graph-sketching strategy box in Subsection 2.4 of Unit 10 for information on how to sketch and label a graph correctly. Question 2 - 10 marks This question is based on your work on MU123 up to and including Unit 10. Jason's father helped him to build a miniature catapult for a history project. To demonstrate how this type of weapon was used in history, Jason releases a water bomb (a small bag of water) from the catapult. The trajectory of the water bomb after it is released from the catapult can be modelled by a quadratic equation of the form y = ar' +br + c where y represents the height (in metres) of the water bomb above the ground, and r represents the horizontal distance (in metres) of the water bomb from the position where it leaves the catapult. You may assume that the surface of the ground is horizontal, and that the water bomb is not affected by wind. (a) The quadratic equation produced to model the trajectory of a water bomb is y = -0.06- + 1.31r + 1.38 In this part of the question, you are asked to consider the graph modelled by this quadratic equation. (i) What does the y-intercept represent in the context of this model? (ii) Use the quadratic formula to find the r-intercepts. Give your answers correct to two decimal places. (b) In a test, Jason's father stands 25m away horizontally from where the water bomb is released. Explain why the water bomb can't possibly hit him. (c) In another test, Jason's father, who is 1.8m tall, moves to a position directly in the path of the water bomb, at a distance of 21m horizontally from where the water bomb is released. Will the water bomb pass over him? Explain your