Quadratic variation of y

If $y$ varies as the sum of three quantities of which the first is constant, the second varies as $x$, and the third as $x^2$; and if $y=0$ when $x=1$, $y=1$ when $x=2$, and $y=4$ when $x=3$, find $y$ when $x=7$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. III. Variation, Examples III, No. 14