Let's look at the graph of the function $y = x^2$. Step 1: This means for any number $x$, $y$ is $x$ times $x$. Step 2: For example, if $x = 2$, then $y = 2^2 = 4$. Step 3: If $x = -1$, then $y = (-1)^2 = 1$. Step 4: The graph is a U-shaped curve called a parabola. Step 5: The lowest point is at $(0,0)$, because $0^2 = 0$. Step 6: The $y$-intercept is where $x=0$, so $y=0$. Step 7: The $x$-intercept is where $y=0$, so $x=0$. Final answer: The graph of $y = x^2$ is a U-shape crossing the origin (0,0).