1. **State the problem:** You are given the height function of a curved arch support: $$f(x) = -0.0009x^2 + 1.24x + 1.65$$ You stand on a platform 2 feet above the maximum height of the arch and want to know if you are safe to bungee jump with a bungee cord that stretches 435 feet. 2. **Find the maximum height of the arch:** The function is a quadratic with a negative leading coefficient, so it opens downward and has a maximum at its vertex. The vertex $x$-coordinate is given by: $$x = -\frac{b}{2a} = -\frac{1.24}{2 \times (-0.0009)} = \frac{1.24}{0.0018} = 688.89$$ 3. **Calculate the maximum height $f(688.89)$:** $$f(688.89) = -0.0009(688.89)^2 + 1.24(688.89) + 1.65$$ Calculate each term: $$-0.0009 \times 688.89^2 = -0.0009 \times 474581.79 = -427.11$$ $$1.24 \times 688.89 = 853.23$$ So, $$f(688.89) = -427.11 + 853.23 + 1.65 = 427.77$$ 4. **Calculate your jump height:** You stand 2 feet above the maximum height, so your jump height is: $$427.77 + 2 = 429.77$$ 5. **Compare jump height to bungee stretch:** The bungee stretches 435 feet, which is greater than your jump height 429.77 feet. 6. **Conclusion:** Since the bungee stretch (435 ft) is greater than your jump height (429.77 ft), you are safe to jump. **Final answer:** You are safe to jump because the bungee cord can stretch farther than your jump height.