Answer
$f(x)=ax^2$.
Work Step by Step
Assume the quadratic is in standard form $f(x)=a(x-h)^2+k$, the vertex $(0,0)$ leads to $h=k=0$, we have $f(x)=ax^2$. The x-intercept is $x=0$ and the y-intercept is $y=0$ meaning all the intercepts are the same point $(0,0)$. Thus the general form is $f(x)=ax^2$.
