Question: how to find x and y intercepts of y=-(x+2)^3
1. **State the problem:** Find the $x$-intercepts and $y$-intercepts of the function $$y=-(x+2)^3$$.
2. **Recall the definitions:**
- The $x$-intercepts occur where $$y=0$$.
- The $y$-intercept occurs where $$x=0$$.
3. **Find the $x$-intercepts:**
Set $$y=0$$:
$$0 = -(x+2)^3$$
This implies:
$$(x+2)^3 = 0$$
Take the cube root of both sides:
$$x+2 = 0$$
Solve for $$x$$:
$$x = -2$$
4. **Find the $y$-intercept:**
Set $$x=0$$ in the original equation:
$$y = -(0+2)^3 = -2^3 = -8$$
5. **Summary:**
- The $x$-intercept is at $$(-2, 0)$$.
- The $y$-intercept is at $$(0, -8)$$.
These points show where the graph crosses the axes.