Coordinate Geometry - Area of Rectilinear Figures

The graph of the quadratic function \(y = \frac{3}{4}x^2 + bx + c\) is symmetrical about the line \(x = 1\) and passes through \(\left(2, -\frac{9}{4}\right)\).

1. Find the values of \(b\) and \(c\).
2. Let \(B\), \(C\) be the points of intersection between the graph of \(y = \frac{3}{4}x^2 + bx + c\) and the \(x\)-axis, where \(B\) is on the left-hand-side of \(C\).
   Find the coordinates of a point \(E\) on the part of the graph of \(y = \frac{3}{4}x^2 + bx + c\) that is below the \(x\)-axis, such that the area of triangle \(BCE\) is a maximum. Hence find this maximum of area.