# Is y=x^2 + 3x - 15 a function?

Yes, it is (in the usual sense that $y$ is a function of $x$).
For any value of $x$, the expression gives only one (never two or more) values for $y$.
Here is the graph on $y = {x}^{2} + 3 x - 15$. As you can see, it passes the vertical line test.
(There are many times that 2 values of $x$ give the same value of $y$, but that is ok for a function.)