this table shows values that represent a quadratic function.\nwhat is the average rate of change for this…

this table shows values that represent a quadratic function.\nwhat is the average rate of change for this quadratic function for the interval from ( x = 4 ) to ( x = 6 )?\na. -20\nb. 20\nc. 10\nd. -10

this table shows values that represent a quadratic function.\nwhat is the average rate of change for this quadratic function for the interval from ( x = 4 ) to ( x = 6 )?\na. -20\nb. 20\nc. 10\nd. -10

Answer

Explanation:

Step1: Recall the average rate of change formula

The average rate of change formula for a function (y = f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 4), (b=6).

Step2: Identify (f(a)) and (f(b)) from the table

When (x = 4), (y=f(4)=-17); when (x = 6), (y = f(6)=-37).

Step3: Substitute values into the formula

Substitute (a = 4), (b = 6), (f(a)=-17), (f(b)=-37) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{-37-(-17)}{6 - 4}=\frac{-37 + 17}{2}).

Step4: Simplify the expression

First, simplify the numerator: (-37+17=-20). Then, (\frac{-20}{2}=-10).

Answer:

D. -10