5. 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 and i'll give you a medal!

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= In this exaple is x1=4 and x2=7 and we will find y1 and y2:
y1=3(4-3)²+4=3*1+4=7
y2=3(7-3)²+4=3*16+4=48+4=52
Finally:
The average rate of change for f(x) from x=4 to x=7 is 15.