Maths Paper 1, November 2024, question 6.2

The diagram below shows the parabola $f(x)=-x^2+2x+8$ and a straight line $g$. The line $g$ cuts the parabola at point A on the left, which lies on the x-axis, and at point C(2;8) on the right. Prove that the straight line $g$ has the equation $g(x)=2x+4$.