If f(x) = x^2 + 2x + 1, what is the vertex of the parabola?

If f(x) = x^2 + 2x + 1, what is the vertex of the parabola?

Correct Answer: (-1, 0)

Step 1: Start with the function f(x) = x^2 + 2x + 1.
Step 2: Recognize that this is a quadratic function, which can be written in the form f(x) = a(x - h)^2 + k, where (h, k) is the vertex.
Step 3: To find the vertex, we can complete the square. First, take the x^2 and 2x terms: x^2 + 2x.
Step 4: To complete the square, take half of the coefficient of x (which is 2), square it (1), and add and subtract it inside the function: f(x) = (x^2 + 2x + 1) - 1 + 1.
Step 5: This simplifies to f(x) = (x + 1)^2, which is now in vertex form.
Step 6: From the vertex form, we can see that the vertex is at the point (-1, 0).

Vertex of a Parabola – The vertex of a parabola represented by a quadratic function can be found by converting the function into vertex form or using the formula for the vertex.
Completing the Square – The process of rewriting a quadratic function in the form f(x) = a(x - h)^2 + k to easily identify the vertex (h, k).