1. **State the problem:** We have the function $f(x) = x^2 - 10x + 28$ and the average rate of change from $x = -8$ to $x = 1$ is given as $-17$. 2. **Formula for average rate of change:** $$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$$ where $a = -8$ and $b = 1$. 3. **Calculate $f(-8)$ and $f(1)$:** $$f(-8) = (-8)^2 - 10(-8) + 28 = 64 + 80 + 28 = 172$$ $$f(1) = 1^2 - 10(1) + 28 = 1 - 10 + 28 = 19$$ 4. **Verify average rate of change:** $$\frac{f(1) - f(-8)}{1 - (-8)} = \frac{19 - 172}{1 + 8} = \frac{-153}{9} = -17$$ This matches the given average rate of change. 5. **Equation of the secant line:** Using point-slope form with point $(-8, 172)$ and slope $-17$: $$y - 172 = -17(x + 8)$$ $$y = -17x - 136 + 172 = -17x + 36$$ 6. **Estimate $f(-5)$ using the secant line:** $$y = -17(-5) + 36 = 85 + 36 = 121$$ This matches Avani's estimate. 7. **Determine if the estimate is an underestimate or overestimate:** The function $f(x) = x^2 - 10x + 28$ is a quadratic with a positive leading coefficient ($1$), so it is **concave up**. 8. **Interpretation:** The secant line between $x = -8$ and $x = 1$ lies **below** the graph of a concave up function between these points. 9. **Conclusion:** The estimate from the average rate of change can best be thought of as a line from $x = -8$ to $x = 1$. Because that line sits **below** the graph, the approximation is an **underestimate**. **Final answer:** The estimate $f(-5) \approx 121$ is an underestimate of the true value because the secant line lies below the concave up parabola between $x = -8$ and $x = 1$.