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The equation provided is \( y = x^2 \), which represents a standard parabola. 

For a parabola in the form \( y = ax^2 + bx + c \), the vertex is located at the point:

\[
x = -\frac{b}{2a}
\]

In this case, since the equation is \( y = x^2 \), we can compare it to the general form. Here, \( a = 1 \), \( b = 0 \), and \( c = 0 \). Thus, the \( x \)-coordinate of the vertex is:

\[
x = -\frac{0}{2(1)} = 0
\]

To find the corresponding \( y \)-coordinate, substitute \( x = 0 \) into the equation \( y = x^2 \):

\[
y = 0^2 = 0
\]

Therefore, the vertex of the parabola \( y = x^2 \) is at the point \( (0, 0) \).

Would you like more details or have any questions? Here are five related questions for practice:

1. What is the vertex of the parabola \( y = 2x^2 + 4x + 1 \)?
2. How does the vertex change if we modify the equation to \( y = -x^2 \)?
3. Can you identify the axis of symmetry for the parabola \( y = x^2 \)?
4. What is the vertex form of a quadratic equation, and how can you rewrite \( y = x^2 \) in that form?
5. How does changing the value of \( a \) in \( y = ax^2 \) affect the graph of the parabola?

**Tip**: The vertex form of a parabola can make identifying the vertex very simple. It is written as \( y = a(x-h)^2 + k \), where \( (h, k) \) is the vertex.

Find the vertex of the parabola y = x^2. Simplify both coordinates and write them as proper fractions, improper fractions, or integers.

Learn how to find the vertex of the parabola y = x^2 with step-by-step guidance. This problem covers key algebraic concepts, such as vertex calculation using the formula x = -b / 2a, and is ideal for students in Grades 8-10.

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