The graphs of y = x² - 3 and y = 4x - 3 intersect at two points. What is the product of the x-coordinates of these two points?

Set the two expressions for $y$ equal: $x^2 - 3 = 4x - 3$. Add 3 to both sides and subtract $4x$: $x^2 - 4x = 0$, which factors as $x(x - 4) = 0$. The intersections are at $x = 0$ and $x = 4$, and the product of the $x$-coordinates is $0 \times 4 = 0$, choice C. Vieta's formulas agree: the product of the roots is the constant term, which is 0. Choice A (4) is the sum of the roots, or the nonzero root. Choice B ($-3$) is the constant from the original equations, which cancels. Choice D (3) is the same constant with a sign slip.