To find the minimum value of the parabola given by the equation $y = x^2$, we need to analyze the characteristics of this quadratic function.

1. Form and Shape: The equation $y = x^2$ represents a parabola that opens upwards, meaning it has a minimum value at its vertex.

2. Vertex of the Parabola: For a parabola in the form $y = ax^2 + bx + c$, the x-coordinate of the vertex is given by $x = -\frac{b}{2a}$. In this case, since $a = 1$ and $b = 0$, the vertex is at $x = 0$.

3. Finding the Minimum Value: Substitute $x = 0$ into the equation $y = x^2$: $y = 0^2 = 0$ So, the minimum value of $y$ is $0$.

4. Conclusion: The minimum value of the parabola $y = x^2$ is $0$.

Would you like more details or have any questions about this?

Here are some related questions:

1. What is the maximum value of the function $y = -x^2$?
2. How do we determine the direction in which a parabola opens?
3. What are the general steps to find the vertex of any quadratic function?
4. How does the value of $a$ in $y = ax^2$ affect the shape of the parabola?
5. Can a parabola with a positive $a$-value ever have a maximum?

Tip: The vertex form of a quadratic function can quickly help you identify the minimum or maximum value by observing the vertex point.