The equation \( x^2 + 2x + 1 \) represents a parabola. To find the vertex, we can first recognize that this quadratic is in the form \( ax^2 + bx + c \).

1. The vertex formula for a parabola given by \( y = ax^2 + bx + c \) is:
   \[
   x_{\text{vertex}} = \frac{-b}{2a}
   \]
   Here, \( a = 1 \), \( b = 2 \), and \( c = 1 \).

2. Applying the formula:
   \[
   x_{\text{vertex}} = \frac{-2}{2(1)} = -1
   \]

3. To find the y-coordinate of the vertex, substitute \( x = -1 \) back into the equation \( y = x^2 + 2x + 1 \):
   \[
   y_{\text{vertex}} = (-1)^2 + 2(-1) + 1 = 1 - 2 + 1 = 0
   \]

Thus, the vertex of the parabola is at \( (-1, 0) \).

Would you like more details on how this formula works or other related information?

Here are some related questions to explore:

1. How can you find the axis of symmetry for a parabola?
2. What is the significance of the vertex in a quadratic function?
3. Can you find the roots of the equation \( x^2 + 2x + 1 \)?
4. How does the direction of the parabola change with different values of \( a \)?
5. What are the steps to convert a quadratic equation into vertex form?

**Tip:** The vertex form of a parabola is useful for identifying the vertex more directly: \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex.

x^2 + 2x + 1 The vertex of the parabola is

Learn how to find the vertex of the quadratic equation x^2 + 2x + 1. This step-by-step guide covers the use of the vertex formula and how to calculate the x and y coordinates of the vertex. Suitable for students in Grades 8-10.

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