1. **State the problem:** We need to order the functions $f(x)$, $g(x)$, and $h(x)$ by their maximum values from smallest to largest. 2. **Find the maximum value of $f(x) = (6 - x)(x - 7)$:** Expand the function: $$f(x) = (6 - x)(x - 7) = 6x - 42 - x^2 + 7x = -x^2 + 13x - 42$$ This is a quadratic function opening downwards (coefficient of $x^2$ is negative), so it has a maximum at the vertex. The vertex $x$-coordinate is given by: $$x = -\frac{b}{2a} = -\frac{13}{2 \times (-1)} = \frac{13}{2} = 6.5$$ Calculate $f(6.5)$: $$f(6.5) = -(6.5)^2 + 13 \times 6.5 - 42 = -42.25 + 84.5 - 42 = 0.25$$ So, the maximum value of $f(x)$ is $0.25$. 3. **Find the maximum value of $g(x)$:** From the table: $$g(-6) = -3, g(-5) = 2, g(-4) = 5, g(-3) = 6, g(-2) = 5, g(-1) = 2, g(0) = -3$$ The maximum value is $6$ at $x = -3$. 4. **Find the maximum value of $h(x)$:** The graph is a downward-opening parabola with vertex approximately at $(-4, 9)$. Therefore, the maximum value of $h(x)$ is approximately $9$. 5. **Order the maximum values:** $$f(x)_{max} = 0.25 < g(x)_{max} = 6 < h(x)_{max} = 9$$ 6. **Final answer:** The order from smallest to largest maximum value is: $$f(x), g(x), h(x)$$