\(f(x) = 9 - (x - 2)^2\)
- Write down the maximum value of \(f(x)\). [1]
- Sketch the graph of \(y = f(x)\), showing the coordinates of the points at which the graph meets the coordinate axes. [5]
The points \(A\) and \(B\) on the graph of \(y = f(x)\) have coordinates \((-2, -7)\) and \((3, 8)\) respectively.
- Find, in the form \(y = mx + c\), an equation of the straight line through \(A\) and \(B\). [4]
- Find the coordinates of the point at which the line \(AB\) crosses the \(x\)-axis. [2]
The mid-point of \(AB\) lies on the line with equation \(y = kx\), where \(k\) is a constant.
- Find the value of \(k\). [2]