1. **State the problem:** We need to draw the graph of the function $y = x^2 - 4$. 2. **Formula and explanation:** The function is a quadratic function of the form $y = ax^2 + bx + c$ where $a=1$, $b=0$, and $c=-4$. 3. **Key features:** - The graph is a parabola opening upwards because $a > 0$. - The vertex is at the point $(h, k)$ where $h = -\frac{b}{2a} = 0$ and $k = c - \frac{b^2}{4a} = -4$. 4. **Find intercepts:** - **y-intercept:** Set $x=0$, then $y = 0^2 - 4 = -4$. - **x-intercepts:** Set $y=0$, solve $x^2 - 4 = 0$. 5. **Solve for x-intercepts:** $$ x^2 - 4 = 0 \\ (x - 2)(x + 2) = 0 \\ x = 2 \text{ or } x = -2 $$ 6. **Summary:** The parabola has vertex at $(0, -4)$, crosses the x-axis at $x=2$ and $x=-2$, and crosses the y-axis at $y=-4$. This is the graph of $y = x^2 - 4$.