1. The function given is $f(x) = -x^2 - x + 6$. 2. To find the equation of $h$, we first reflect $f$ about the x-axis. Reflection about the x-axis changes $f(x)$ to $-f(x)$. $$-f(x) = -(-x^2 - x + 6) = x^2 + x - 6$$ 3. Next, translate this reflected function 3 units to the right. A translation 3 units to the right replaces $x$ by $x - 3$. $$h(x) = (x - 3)^2 + (x - 3) - 6$$ 4. Expand and simplify: $$(x - 3)^2 = x^2 - 6x + 9$$ So, $$h(x) = x^2 - 6x + 9 + x - 3 - 6 = x^2 - 5x + 0$$ 5. Now, write $h(x)$ in the form $a(x + p)^2 + q$ by completing the square: $$h(x) = x^2 - 5x$$ Complete the square: $$x^2 - 5x = (x^2 - 5x + \frac{25}{4}) - \frac{25}{4} = \left(x - \frac{5}{2}\right)^2 - \frac{25}{4}$$ 6. Therefore, $$h(x) = \left(x - \frac{5}{2}\right)^2 - \frac{25}{4}$$ 7. Rewrite $h(x)$ in the form $a(x + p)^2 + q$: $$h(x) = 1 \cdot \left(x + \left(-\frac{5}{2}\right)\right)^2 - \frac{25}{4}$$ So, $$h(x) = (x + (-\frac{5}{2}))^2 - \frac{25}{4}$$ Final answer: $$h(x) = (x - \frac{5}{2})^2 - \frac{25}{4}$$