mu123 maths

{a} This part of the question concerns the quadratic equation tx3+2sz4g=u. [i] Find the discriminant of the quadratic apt-mien 4::2 + 23,-: 49. {ii} What does this tell you about the number of solutions of the equation? Explain your answer briey. [iii] What duet this tell you about the graph of y = 4:3 + 23.1: 49? {b} Figure 1 shoes part of the graph of the quadratic hmction y = 12 + 5.1: 6. -6 1=x' + 5x -6Figure 1 (i) Find the equation of the axis of symmetry of the parabola given by y = x2 +5x -6, explaining your method. (ii) Use your answer to part (b) (i) to find the coordinates of the vertex of the parabola given by y = r- +5r - 6.(c) This part of the question concerns the quadratic function y =x- +18r + 70. (i) Write the quadratic expression r2 + 18r + 70 in completed-square form. (ii) Use the completed-square form from part (c) (i) to solve the equation r- + 181 + 70 =0, leaving your answer in exact (surd) form. (iii) Use the completed-square form from part (c) (i) to write down the vertex of the parabola y = x2 + 181 + 70. (iv) Provide a sketch of the graph of the parabola y = 2- + 18x + 70, either by hand or by using a suitable graphing software package like Graphplotter. If you intend to go on to study more mathematics, you are advised to sketch by hand. 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