1. **State the problem:** We have the height function of an object launched from a platform given by $$f(x) = -16x^2 + 64x + 6$$ where $x$ is time in seconds and $f(x)$ is height in feet. We need to determine which statements A to E are true. 2. **Recall the quadratic formula and properties:** The function is a quadratic with $a = -16$, $b = 64$, and $c = 6$. Since $a < 0$, the parabola opens downward, so it has a maximum point. 3. **Find the height at 1 second (for statement A):** $$f(1) = -16(1)^2 + 64(1) + 6 = -16 + 64 + 6 = 54$$ Since 54 is less than 60, statement A is false. 4. **Find the time of maximum height (for statement B):** The vertex time is given by $$x = -\frac{b}{2a} = -\frac{64}{2 \times (-16)} = -\frac{64}{-32} = 2$$ So the object reaches maximum height at 2 seconds, statement B is true. 5. **Find the maximum height (for statement C):** Calculate $$f(2) = -16(2)^2 + 64(2) + 6 = -16(4) + 128 + 6 = -64 + 128 + 6 = 70$$ The maximum height is 70 feet, so statement C is true. 6. **Height of the platform (for statement D):** The height at time zero is the platform height: $$f(0) = -16(0)^2 + 64(0) + 6 = 6$$ So the platform height is 6 feet, statement D is true. 7. **Height behavior over time (for statement E):** Since the parabola opens downward, the height increases until the vertex at 2 seconds, then decreases afterward. So statement E is true. **Final answers:** - A: False - B: True - C: True - D: True - E: True