Find the domain and the set of values of the function y = x ^ 2-4x + 4.

We have a function:

y = x ^ 2 – 4 * x + 4.

The function is quadratic, the graph is a parabola, the branches of which are directed upwards.

There are no restrictions, the scope of the function is any number.

To determine the range of values, we derive the square of the binomial:

x ^ 2 – 4 * x + 4 = x ^ 2 – 2 * x * 2 + 2 ^ 2 = (x – 2) ^ 2.

As you can see, there is a square of a binomial, which takes non-negative values regardless of the value of the argument, which means:

y> = 0 – range of values of the function.