Function/Curve that goes through certain points?

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A method to create a function that passes through specific points involves using polynomial equations. For example, a function can be constructed to cross y=0 at designated x-coordinates by multiplying factors corresponding to those points. The provided example illustrates this with the function f(x)=(x+10)(x+2)(x-5), which crosses y=0 at x=-10, x=-2, and x=5. This approach is straightforward and allows for expansion to include more points. The discussion highlights the utility of polynomial functions in curve fitting.
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Is there a simple way to make a function go through a set of points?

Something similar to what I'm looking for is this; a function that creates a smooth curve crossing y=0 at a list of x-coordinates

This will cross y=0 at x=-10, x=-2, and x=5
f(x)=(x-(-10))(x-(-2))(x-(5))

This is simple and infinitely expandable. Thanks!
 
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