To find the intercepts of the equation $y = x^2 - 4$, we need to determine where the graph crosses the x-axis and the y-axis.

X-intercepts:

X-intercepts occur where $y = 0$. So, set $y = 0$ and solve for $x$:

$0 = x^2 - 4$

This simplifies to:

$x^2 = 4$

Taking the square root of both sides:

$x = \pm 2$

Thus, the x-intercepts are at $(2, 0)$ and $(-2, 0)$.

Y-intercept:

The y-intercept occurs where $x = 0$. Plug $x = 0$ into the equation:

$y = 0^2 - 4 = -4$

Thus, the y-intercept is at $(0, -4)$.

Intercepts:

• X-intercepts: $(2, 0)$ and $(-2, 0)$
• Y-intercept: $(0, -4)$

Would you like to see the graph, or do you have any questions about the solution?

Here are 5 questions to expand your understanding:

1. How would the graph change if the equation was $y = x^2 + 4$?
2. What would the intercepts be if the equation was $y = x^2 - 9$?
3. What is the vertex of the parabola represented by $y = x^2 - 4$?
4. How do the intercepts relate to the symmetry of the parabola?
5. Can you find the axis of symmetry for the parabola?

Tip: When solving for x-intercepts, always remember to set $y = 0$ and solve for $x$.