The figure shows the curve \(y = x^2\) and the straight line \(2x + y = 15\). Find

  1. the co-ordinates of \(P\) and \(Q\),
  2. the area of the shaded region.
A plot of the curve $y = x^2$ and the line $2x + y = 15$ with $-8.5 \le x \le 8.5$. The point in the first quadrant at which the curve and line cross is denoted by $P$. The $x$-intercept of the line is denoted by $Q$. The shaded region is the region beneath both the curve and line and between the origin and $Q$.