Question

this table shows values that represent a quadratic function. what is the average rate of change for this quadratic function for the interval from x = 4 to x = 6? a. -20 b. 20 c. 10 d. -10

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: Find \(f(4)\) and \(f(6)\) from the table

From the table, when \(x = 4\), \(y=f(4)=-17\); when \(x = 6\), \(y = f(6)=-37\).

Step3: Substitute values into the formula

Substitute \(a = 4\), \(b = 6\), \(f(4)=-17\), \(f(6)=-37\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{-37-(-17)}{6 - 4}=\frac{-37 + 17}{2}=\frac{-20}{2}\).

Answer:

D. -10