1. **State the problem:** We are given the quadratic function $$f(x) = -0.04x^2 + 0.48x - 0.8$$ representing the company's expected net worth over time in years. 2. **Find when the net worth is zero:** The equivalent factored form is $$f(x) = -0.04(x - 2)(x - 10)$$. 3. **Use the factored form to find zeros:** Set $$f(x) = 0$$: $$0 = -0.04(x - 2)(x - 10)$$ Since $$-0.04 \neq 0$$, we have: $$(x - 2)(x - 10) = 0$$ This gives two solutions: $$x - 2 = 0 \Rightarrow x = 2$$ $$x - 10 = 0 \Rightarrow x = 10$$ 4. **Interpretation:** The company's expected net worth is zero after **2 years** and after **10 years**. 5. **Find the maximum expected net worth:** The vertex form is given as: $$f(x) = -0.04(x - 6)^2 + 0.64$$ 6. **Identify the vertex:** The vertex of a parabola in form $$a(x - h)^2 + k$$ is at $$(h, k)$$. Here, $$h = 6$$ and $$k = 0.64$$. 7. **Interpretation:** The maximum expected net worth is $$0.64$$ million dollars, which occurs after **6 years**. **Final answers:** - The company's expected net worth is zero after **2** years and after **10** years. - The company's maximum expected net worth is **0.64** million dollars, which occurs after **6** years.