1. The problem is to analyze the function $y = x^2$. 2. This is a quadratic function, which generally has the form $y = ax^2 + bx + c$. Here, $a=1$, $b=0$, and $c=0$. 3. The graph of $y = x^2$ is a parabola opening upwards because $a > 0$. 4. The vertex of the parabola is at the origin $(0,0)$, which is also the minimum point. 5. The y-intercept is found by evaluating $y$ at $x=0$: $y = 0^2 = 0$. 6. The x-intercepts are found by solving $x^2 = 0$, which gives $x=0$. 7. The function is symmetric about the y-axis because it is an even function. 8. The domain of $y = x^2$ is all real numbers, and the range is $y \geq 0$. 9. Summary: The parabola $y = x^2$ has vertex at $(0,0)$, opens upwards, and intercepts at $(0,0)$.