Final answer:
To calculate the average rate of change for the given equation over the interval -1, substitute x-values -1 and -2 into the equation to find y-values, and then calculate the difference in y-values and x-values. The average rate of change is -21.
Step-by-step explanation:
To calculate the average rate of change for the equation y = 3x^2 – 12x + 17 over the interval -1, we need to find the difference in y-values and x-values between the given point (-1) and another point on the curve. Let's choose another point, for example, (-2).
Substituting x = -1 into the equation, we get:
y = 3(-1)^2 – 12(-1) + 17 = 3 + 12 + 17 = 32
Similarly, substituting x = -2 into the equation, we get:
y = 3(-2)^2 – 12(-2) + 17 = 12 + 24 + 17 = 53
The difference in y-values is 53 - 32 = 21, and the difference in x-values is -2 - (-1) = -1.
Therefore, the average rate of change is 21/-1 = -21.