12. The parabola with its axis of symmetry parallel to the $y$-axis, passing through the points $(1,0)$ and $(4,0)$, and tangent to the line $y=2x$ is . $\qquad$
12. $y=-\frac{2}{9}(x-1)(x-4)$ or $y=-2(x-1)(x-4)$. Hint: We can set it as $y=a(x-1)(x-4)$ and combine with $y=$ $2 x$, eliminate $y$, and by $\Delta=0$, solve for $a=-\frac{2}{9}$ or -2.