Express \(( x - 5 ) ( x - 3 ) + 2\) in the form \(( x - p ) ^ { 2 } + q\), where \(p\) and \(q\) are integers.
(3 marks)
Sketch the graph of \(y = ( x - 5 ) ( x - 3 ) + 2\), stating the coordinates of the minimum point and the point where the graph crosses the \(y\)-axis.
Write down an equation of the tangent to the graph of \(y = ( x - 5 ) ( x - 3 ) + 2\) at its vertex.
Describe the geometrical transformation that maps the graph of \(y = x ^ { 2 }\) onto the graph of \(y = ( x - 5 ) ( x - 3 ) + 2\).