Findtheminimumvalueoftheparabolay = x2 − 4x.Simplify your answer and write it as a proper fraction, improper fraction, or integer.

To find the minimum value of the parabola y = x^2 - 4x, we first need to complete the square.

The equation y = x^2 - 4x can be rewritten as y = (x^2 - 4x + 4) - 4 by adding and subtracting 4. This is because the term 4x in the middle can be split into 2*2x, and the square of 2 is 4.

So, y = (x - 2)^2 - 4.

This is a standard form of a parabola, y = (x - h)^2 + k, where (h, k) is the vertex of the parabola.

In this case, h = 2 and k = -4.

Since the coefficient of x^2 is positive, the parabola opens upwards, and thus, the vertex of the parabola is its minimum point.

So, the minimum value of the parabola y = x^2 - 4x is k = -4.