0580 P42 - Jun 2015 - Q5 - 16 marks
15329
\(y=x^2-2x+12/x,\quad x\ne0\).
| \(x\) | -4 | -3 | -2 | -1 | -0.5 | 0.5 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|---|---|---|
| \(y\) | 21 | 11 | -9 | -22.75 | 23.25 | 11 | 6 | 11 |
(a) Complete the table. [2]
(b) Draw the graph for \(-4\le x\le-0.5\) and \(0.5\le x\le4\). [5]
(c) Draw a tangent to estimate the gradient at (1, 11). [3]
\(x^2-2x+12/x=k\) has exactly two distinct solutions. Use the graph to find:
(d(i)) the value of k; [1]
(d(ii)) the two solutions. [2]
(e) \(x^3+ax^2+bx+c=0\) can be solved by drawing \(y=3x+1\). Find a, b and c. [3]
