The function f(x) = x² + 2x + 1 is a quadratic function that can be rewritten in vertex form to find its axis of symmetry. To do this, we can complete the square or use the standard formula for the axis of symmetry of a quadratic function.
For the general form of a quadratic function, f(x) = ax² + bx + c, the axis of symmetry can be found using the formula:
x = -b / (2a)
In the given function, a = 1 and b = 2. Plugging these values into the formula gives us:
x = -2 / (2 * 1) = -1
This means the axis of symmetry is the vertical line x = -1. To visualize this, you typically would draw the function on a graph. The axis of symmetry will be a dashed line that runs vertically through x = -1, dividing the parabola into two symmetrical halves.
So, when looking at potential graph options, you should select the one that features a vertical line at x = -1 as the axis of symmetry for the function f(x) = x² + 2x + 1.