1. The problem is to draw a hyperbolic diagram for the function $y = x^2$. 2. The function $y = x^2$ is a parabola, not a hyperbola. A hyperbola has the form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ or $\frac{y^2}{b^2} - \frac{x^2}{a^2} = 1$. 3. Since $y = x^2$ is a parabola, we can plot it to understand its shape. It opens upwards with vertex at the origin $(0,0)$. 4. The graph is symmetric about the y-axis. 5. To plot, pick values of $x$ and compute $y$: for example, $x = -2, y = 4$; $x = -1, y = 1$; $x = 0, y = 0$; $x = 1, y = 1$; $x = 2, y = 4$. 6. Plot these points and draw a smooth curve through them to get the parabola shape. Final answer: The function $y = x^2$ is a parabola, not a hyperbola, and its graph is symmetric about the y-axis with vertex at the origin.