Question 4 - A-Level Maths

Express \(x ^ { 2 } + 5 x + 7\) in the form \(( x + p ) ^ { 2 } + q\), where \(p\) and \(q\) are rational numbers.
(3 marks)
A curve has equation \(y = x ^ { 2 } + 5 x + 7\).
1. Find the coordinates of the vertex of the curve.
2. State the equation of the line of symmetry of the curve.
3. Sketch the curve, stating the value of the intercept on the \(y\)-axis.
Describe the geometrical transformation that maps the graph of \(y = x ^ { 2 }\) onto the graph of \(y = x ^ { 2 } + 5 x + 7\).