Quadratic Function 84E426

1. **State the problem:** We are given the function $$f(t) = -16t^2 + 22t + 4$$ which models the height of a bean bag over time. We need to identify the function family to which $f$ belongs. 2. **Recall the function families:** Common function families include linear, quadratic, cubic, exponential, etc. The general form of a quadratic function is $$ax^2 + bx + c$$ where $a$, $b$, and $c$ are constants and $a \neq 0$. 3. **Analyze the given function:** The function $$f(t) = -16t^2 + 22t + 4$$ has a term with $t^2$, a term with $t$, and a constant term. The highest power of $t$ is 2. 4. **Conclusion:** Since the highest power of $t$ is 2 and the function matches the form $$ax^2 + bx + c$$, the function $f$ belongs to the **quadratic function family**. 5. **Additional note:** The coefficient of $t^2$ is negative ($-16$), so the parabola opens downward, which matches the description of the bean bag's height peaking and then decreasing.