Question 4 - A-Level Maths

Write \(2 x ^ { 2 } + 6 x + 7\) in the form \(p ( x + q ) ^ { 2 } + r\), where \(p , q\) and \(r\) are constants.
State the coordinates of the minimum point on the graph of \(y = 2 x ^ { 2 } + 6 x + 7\).
Hence deduce
- the minimum value of \(2 \tan ^ { 2 } \theta + 6 \tan \theta + 7\),
- the smallest positive value of \(\theta\), in degrees, for which the minimum value occurs.