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The equation given is \( y = x^2 \), which represents a standard form of a parabola. In this case, the equation is in the form \( y = ax^2 + bx + c \), where \( a = 1 \), \( b = 0 \), and \( c = 0 \).

For a parabola in the form \( y = ax^2 + bx + c \), the vertex can be found using the formula:

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

Since \( b = 0 \), the \( x \)-coordinate of the vertex is:

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

Now, substitute \( x = 0 \) into the original equation to find the \( y \)-coordinate:

\[
y = (0)^2 = 0
\]

Thus, the coordinates of the vertex are \( (0, 0) \).

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

Do you want further details or have any questions?

Here are five related questions to expand on this topic:

1. How does changing the value of \( a \) affect the shape of the parabola?
2. What is the significance of the vertex in a quadratic function?
3. How can you derive the equation of a parabola given its vertex and one point on the curve?
4. What happens to the graph of \( y = x^2 \) if you add a constant term \( c \) to the equation?
5. How do you determine whether the vertex is a maximum or minimum?

**Tip:** The vertex is the turning point of the parabola, and for \( y = x^2 \), the vertex is always at the lowest point (minimum) since the parabola opens upwards.

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x, y) point. y = x^2

Learn how to find the vertex of the quadratic function y = x^2 algebraically. This problem demonstrates key algebraic concepts such as quadratic functions and the vertex formula. Suitable for students in Grades 8-10.

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