The equation of the parabola with vertex at origin, which passes through the point $(-3, 7)$ and axis along the x-axis is 

Let a parabola with vertex at origin and axis along the x-axis be $y^2=4ax$. It passes through $(-3, 7)$

hence $(7{)}^2=4a(-3)\Rightarrow a=-\frac{49}{12}.$

$\therefore$ The required equation of the parabola is

$y^2=4\left(-\frac{49}{12}\right)x\text{ or }3y^2=-49x$