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  1. Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7. my equation is F(x) = 3 (x-3)^2 + 4 in vertex form and and y = 3x^2 - 18x +31. Any ideas how to do this would be super helpful and I'll give you a medal!

Verified Answer :

HomertheGenius

The average rate of change of function describes the average rate at which y-value ( or f(x)) is changing with respect to changing x-value.
The average rate of change=\(\frac{ y_{1}- y_{2} }{ x_{1} - x_{2} }\) In this exaple is x1=4 and x2=7 and we will find y1 and y2:
y1=3(4-3)²+4=31+4=7
y2=3(7-3)²+4=316+4=48+4=52
Finally:\(\frac{52-7}{7-4}= \frac{45}{3} =15\)
Answer: The average rate of change for f(x) from x=4 to x=7 is 15.

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