Answer
The equation of a parabola is
$$
x^{2}-4x +y=0
$$
Work Step by Step
The standard form of the equation of a parabola, with vertex : $(2,4)$ and $(0,0) , (4,0)$ are points on the parabola , is
$$
(x-2)^{2}=4p(y-4) ,\ (*) \, \,\ \text {vertical axis form}
$$
since the point $(0,0)$ on parabola then it satisfy its equation as follows :
$$
(0-2)^{2}=4p(0-4)
$$
this implies that
$$
p=-\frac{1}{4}
$$
substituting in equation (*) we obtain
$$
(x-2)^{2}=4 . (-\frac{1}{4} ).(y-4) = 4-y.
$$
Simplify, we have the equation of a parabola in the form:
$$
x^{2}-4x +y=0
$$
