Question 1 - 20 marks 08 August 2023 (c) This part of the question concerns the quadratic function This question is based on your work on MU123 up to and including Unit 10. y = 212- 16x + 14. (a) This part of the question concerns the quadratic equation i) Write the quadratic expression 212 - 16x + 14 in completed-square [2] -312 + 1+2=0. form showing your working. ii) Use the completed-square form from part (c) (i) to solve the [3] (i) Find the discriminant of the quadratic expression -3x2 + x + 2. equation 2x2 - 16z + 14 = 0. (ii) What does this discriminant tell you about the number of solutions [2] (iii) Use the completed-square form from part (c)(i) to write down the [1] of the equation? Explain your answer briefly. coordinates of the vertex of the parabola y = 212 - 16: + 14. (iii) What does this discriminant tell you about the graph of [2] (iv) Provide a sketch of the graph of the parabola y = 2x2 - 162 + 14, y= -3x2 +x+2? either by hand or by using a suitable graphing software package [1] like Graphplotter. (b) Figure 1 shows part of the graph of the quadratic function If you intend to go on to study more mathematics, then you are y = 212 - 8x +6. advised to sketch by hand for the practice. Whichever method you choose, you should refer to the graph-sketching strategy bot 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. Tom likes to play with his toy catapult. He uses an open-top cardboard box as a make-believe model castle. His model castle has a square base of side length 1.0 metre, and the height of each of its walls is 0.3 metres. Lying on the ground, Tom positions the catapult 1.5 metres directly in front of one of the castle walls and decides to launch a projectile towards it. The trajectory of the projectile after it is launched by the catapult can be modelled by an equation of the following form: y = ax +br + c where y represents the height (in metres) of the projectile above the ground, (1,0) (3,0) and I represents the horizontal distance (in metres) of the projectile from the position where it was launched. The values of a, b and c are determined by how the catapult launches the projectile. You may assume that the surface where the catapult and the model castle are placed is completely flat and horizontal. (a) The equation produced to model the trajectory of the projectile is Figure 1 y = -0.16x2+ 0.34x + 0.2 (i) Explain why the graph of the quadratic function y = 2x2 - 8x + 6 [1] In this part of the question, you are asked to consider the graph is u-shaped. [1] modelled by this quadratic equation. (ii) Write down the y-intercept. (i) What does the y-intercept represent in the context of this model? (iii) Using information from the graph, find the equation of the axis of [2] [1] ii) Use the quadratic formula to find the -intercepts. Give your symmetry of the parabola given by y = 2x2 - 8x + 6. answers correct to two decimal places. (iv) Use your answer to part (b)(iii) to find the coordinates of the [2] [4] (b) When the projectile flies over the wall of the castle that is closest to vertex of the parabola given by y = 212 - 8x + 6. Tom, how high above the top of the wall does it pass? (2] (c) What is the maximum height reached by the projectile during its trajectory? [3] page 4 of 13