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 5302 2130 + 29 : 0. (i) Find the discriminant of the quadratic expression 5x2 2100 + 29. (ii) What does this discriminant tell you about the number of solutions of the equation? Explain your answer briey. (iii) What does this discriminant tell you about the graph of y : 5302 21x + 29? (b) Figure 1 shows part of the graph of the quadratic function y : x2 4x 45. Figure 1 (i) Explain why the graph of the quadratic function y : x2 400 45 is ushaped. (ii) Write down the yintercept. (iii) Find the equation of the axis of symmetry of the parabola given by y : x2 4x 45, explaining your method. (iv) Use your answer to part (b)(iii) to nd the coordinates of the vertex of the parabola given by y : x2 4x 45. (c) This part of the question concerns the quadratic function y:x2+14x+36. Write the quadratic expression 002 + 1400 + 36 in completedsquare form. Use the completedsquare form from part (c) (i) to solve the equation 002 + 1490 + 36 : 0, leaving your answer in exact (surd) form. Use the completedsquare form from part (c) (i) to write down the coordinates of the vertex of the parabola y : x2 + 1400 + 36. Provide a sketch of the graph of the parabola y : 002 + 1400 + 36, 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 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