A quadratic function is given by \(\mathrm { f } ( x ) = x ^ { 2 } - 6 x + 8\).
Sketch the graph of \(y = \mathrm { f } ( x )\), giving the coordinates of the points where it crosses the axes. Mark the lowest point on the curve, and give its coordinates.
Solve the inequality \(x ^ { 2 } - 6 x + 8 < 0\).
On the same graph, sketch \(y = \mathrm { f } ( x + 3 )\).
The graph of \(y = \mathrm { f } ( x + 3 ) - 2\) is obtained from the graph of \(y = \mathrm { f } ( x )\) by a transformation. Describe the transformation and sketch the curve on the same axes as in (i) and (iii) above. Label all these curves clearly.