Final answer:
The equation of the parabola in vertex form is y = (x - 4)^2 - 3.
Step-by-step explanation:
The equation of a parabola in vertex form is given by y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Given that the vertex is (4, -3) and the point (2, -1) is on the parabola, we can substitute these values into the equation to solve for 'a'.
-1 = a(2 - 4)^2 + (-3)
-1 = a(-2)^2 - 3
-1 = 4a - 3
4 = 4a
a = 1
Therefore, the equation of the parabola in vertex form is y = (x - 4)^2 - 3.