(a) To express \(y = 4x^2 + 20x + 6\) in the form \(y = a(x + b)^2 + c\), complete the square:

Factor out 4 from the quadratic terms: \(y = 4(x^2 + 5x) + 6\).

Complete the square for \(x^2 + 5x\):

\(x^2 + 5x = (x + \frac{5}{2})^2 - (\frac{5}{2})^2\).

Substitute back: \(y = 4((x + \frac{5}{2})^2 - \frac{25}{4}) + 6\).

Simplify: \(y = 4(x + \frac{5}{2})^2 - 25 + 6\).

\(y = 4(x + \frac{5}{2})^2 - 19\).

(b) Solve \(4(x + \frac{5}{2})^2 - 19 = 45\):

\(4(x + \frac{5}{2})^2 = 64\).

\((x + \frac{5}{2})^2 = 16\).

\(x + \frac{5}{2} = \pm 4\).

\(x = -\frac{5}{2} + 4 = \frac{3}{2}\) or \(x = -\frac{5}{2} - 4 = -\frac{13}{2}\).

(c) The stationary point is at \(x = -\frac{5}{2}\), giving \(y = -19\).

Stationary point: \((-\frac{5}{2}, -19)\).