1. The problem is to analyze the function $y = x^2$ and understand its graph. 2. The formula used is $y = x^2$, which represents a parabola opening upwards. 3. Important rules: - The vertex of the parabola is at the origin $(0,0)$. - The parabola is symmetric about the y-axis. - For any $x$, $y$ is always non-negative since it is a square. 4. Intermediate work: - At $x = -2$, $y = (-2)^2 = 4$. - At $x = -1$, $y = (-1)^2 = 1$. - At $x = 0$, $y = 0^2 = 0$. - At $x = 1$, $y = 1^2 = 1$. - At $x = 2$, $y = 2^2 = 4$. 5. Explanation: The parabola opens upwards because the coefficient of $x^2$ is positive. The vertex at $(0,0)$ is the minimum point. The graph is symmetric about the y-axis, so points on the left and right of the y-axis have the same $y$ value. Final answer: The graph of $y = x^2$ is a parabola opening upwards with vertex at $(0,0)$ and passes through points $(-2,4)$, $(-1,1)$, $(0,0)$, $(1,1)$, and $(2,4)$.