Let's graph the function $y = x^2 - 4$ step by step. 1. This is a parabola that opens upwards because $x^2$ is positive. 2. The $-4$ moves the graph down 4 units. 3. To find the y-intercept, set $x = 0$: $y = 0^2 - 4 = -4$. 4. To find the x-intercepts, set $y = 0$: $0 = x^2 - 4$. 5. Add 4 to both sides: $x^2 = 4$. 6. Take the square root: $x = 2$ or $x = -2$. So, the x-intercepts are at $(2, 0)$ and $(-2, 0)$, and the y-intercept is at $(0, -4)$. The lowest point (vertex) is at $(0, -4)$. Final answer: The graph is a U-shaped curve with vertex at $(0, -4)$, crossing the x-axis at $(2, 0)$ and $(-2, 0)$, and crossing the y-axis at $(0, -4)$.