Find the equation of the parabola joined smoothly to the straight line y=2x at the point P(2,4) as shown below. The parabola passes through the point(5,1).

$\displaystyle y = a(x - b)^2 + c$

$\displaystyle y = a(x - 2)^2 + 4$

$\displaystyle 1 = a(5 - 2)^2 + 4$

$\displaystyle 1 = a(3)^2 + 4$

$\displaystyle 1 = 9a + 4$

$\displaystyle a = \frac{-1}{3}$

$\displaystyle y = \frac{-1}{3}(x - 2)^2 + 4$