1. **State the problem:** We need to find the maximum height of the kangaroo's jump modeled by the function $h(t) = -16t^2 + 24t$. 2. **Identify the type of function:** This is a quadratic function in the form $h(t) = at^2 + bt + c$ where $a = -16$, $b = 24$, and $c = 0$. 3. **Recall the formula for the vertex:** The maximum or minimum of a quadratic function occurs at $t = -\frac{b}{2a}$. 4. **Calculate the time at maximum height:** $$t = -\frac{24}{2 \times -16} = -\frac{24}{-32} = \frac{24}{32} = \frac{3}{4}$$ 5. **Find the maximum height by substituting $t = \frac{3}{4}$ into $h(t)$:** $$h\left(\frac{3}{4}\right) = -16\left(\frac{3}{4}\right)^2 + 24\left(\frac{3}{4}\right)$$ $$= -16 \times \frac{9}{16} + 24 \times \frac{3}{4}$$ $$= \cancel{-16} \times \frac{9}{\cancel{16}} + 24 \times \frac{3}{4}$$ $$= -9 + 18 = 9$$ 6. **Conclusion:** The maximum height of the jump is 9 feet. **Final answer:** 9 ft