How do you find the equation for a curve between two points?

The curve I have is a quadratic that passes through the points $x = - 3$, $x = 2$, and $y = - 3$. I need to find the equation of the curve between $x = - 3$ and $x = 2$.

There could be innumerable curves (though there would be only one line) between two points. You need to find the equation of the curve between x=−3, $x = 2$ and $y = - 3$. These do not even indicate points but three lines and hence information provided is insufficient for finding equation of the curve.