Find the equation, (f(x) = a(x - h)2 + k), for a parabola containing point (2, -1) and having (4, -3) as a vertex. What is the standard form of the equation?

Given that the vertex of the parabola is (4,-3)

The parabola passes through the point (2,-1)

We need to determine the standard form of the equation of the parabola.

Standard form of the equation of the parabola:

The standard form of the equation is where the vertex is (h,k) and a is the constant.

Substituting the vertex (4,-3) in the above equation, we get;

 ---------------(1)

Substituting the point (2,-1) in the above equation, we have;

Thus, the value of a is

Substituting the value of a in the equation (1), we get;

Thus, the standard form of the equation of the parabola is