The problem asks to graph the equation $y = x^2 - 4$.

1. Problem Description

The problem asks to graph the equation $y = x^2 - 4$.

2. Solution Steps

The given equation $y = x^2 - 4$ represents a parabola.

To graph the parabola, we can identify some key features:

- The vertex: The general form of a parabola is $y = a(x-h)^2 + k$, where $(h,k)$ is the vertex. In our case, $y = x^2 - 4 = 1(x-0)^2 - 4$. Thus, the vertex is at $(0, -4)$.

- The y-intercept: To find the y-intercept, set $x=0$ in the equation: $y = (0)^2 - 4 = -4$. The y-intercept is $(0, -4)$, which is also the vertex.

- The x-intercepts: To find the x-intercepts, set $y=0$ in the equation: $0 = x^2 - 4$. Thus, $x^2 = 4$, which implies $x = \pm 2$. The x-intercepts are $(-2, 0)$ and $(2, 0)$.

- Choose a few more points to plot. For instance, when $x = 1$, $y = 1^2 - 4 = -3$. When $x=-1$, $y = (-1)^2 - 4 = -3$. When $x = 3$, $y = 3^2 - 4 = 5$. When $x=-3$, $y = (-3)^2 - 4 = 5$.

Plot these points and draw a smooth curve through them to represent the parabola.

3. Final Answer

The graph of $y = x^2 - 4$ is a parabola with vertex at $(0, -4)$, y-intercept at $(0, -4)$, and x-intercepts at $(-2, 0)$ and $(2, 0)$.