1. Problem: Find the equation of the parabola with vertex (3,1) and passing through point (4,0). 2. Formula: The vertex form of a parabola is $$y = a(x - h)^2 + k$$ where $(h,k)$ is the vertex. 3. Substitute vertex $(3,1)$: $$y = a(x - 3)^2 + 1$$ 4. Use point $(4,0)$ to find $a$: $$0 = a(4 - 3)^2 + 1$$ $$0 = a(1)^2 + 1$$ $$0 = a + 1$$ $$a = -1$$ 5. Final equation: $$y = -1(x - 3)^2 + 1$$ 6. Simplify: $$y = -(x - 3)^2 + 1$$ Answer: The parabola equation is $$y = -(x - 3)^2 + 1$$