1. **Problem statement:** Find the intersection points of the functions $f(x) = -3x$ and $g(x) = x^2$. 2. **Set the functions equal to find intersection points:** $$-3x = x^2$$ 3. **Rewrite the equation:** $$x^2 + 3x = 0$$ 4. **Factor the equation:** $$x(x + 3) = 0$$ 5. **Solve for $x$:** - $x = 0$ - $x + 3 = 0 \Rightarrow x = -3$ 6. **Find corresponding $y$ values by substituting $x$ into either function (use $f(x)$):** - For $x=0$: $f(0) = -3 \cdot 0 = 0$ - For $x=-3$: $f(-3) = -3 \cdot (-3) = 9$ 7. **Intersection points:** $$ (0,0) \quad \text{and} \quad (-3,9) $$