Let's draw the graph of the function $y = x^2 - 4$. Step 1: This is a parabola that opens up because $x^2$ is positive. Step 2: The $-4$ moves the whole graph down by 4 units. Step 3: To find the $y$-intercept, put $x=0$: $y = 0^2 - 4 = -4$. Step 4: To find the $x$-intercepts, put $y=0$: $0 = x^2 - 4$. Step 5: Solve $x^2 = 4$, so $x = 2$ or $x = -2$. The graph crosses the $y$-axis at $(0, -4)$ and the $x$-axis at $(2, 0)$ and $(-2, 0)$. Final answer: The graph is $y = x^2 - 4$ with $x$-intercepts at $(-2, 0)$ and $(2, 0)$, and $y$-intercept at $(0, -4)$.