What type of function is x²+2x+1?

The function f(x) = x^2 + x + 1 is a quadratic function. This is because it has a degree of 2, meaning the highest power of x in the function is 2. Furthermore, the general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants. In this case, a = 1, b = 1, and c = 1, so the function matches this form. Quadratic functions are also characterized by a U-shape when graphed, and this function satisfies that characteristic as well. Therefore, f(x) = x^2 + x + 1 is a quadratic function.