To calculate the average rate of change of the function \( f(x) = x^2 - 3x + 2 \) over the interval \([-2, 1]\), we use the formula for the average rate of change:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = -2 \) and \( b = 1 \).
Step 1: Calculate \( f(-2) \)
\[ f(-2) = (-2)^2 - 3(-2) + 2 = 4 + 6 + 2 = 12 \]
Step 2: Calculate \( f(1) \)
\[ f(1) = (1)^2 - 3(1) + 2 = 1 - 3 + 2 = 0 \]
Step 3: Substitute into the average rate of change formula
\[ \text{Average Rate of Change} = \frac{f(1) - f(-2)}{1 - (-2)} = \frac{0 - 12}{1 + 2} = \frac{-12}{3} = -4 \]
Therefore, the average rate of change of the function \( f(x) = x^2 - 3x + 2 \) over the interval \([-2, 1]\) is \(-4\).
Final answer: −4.