Question

Use the values in the table that represent a quadratic function. x f(x) −1 −13 0 −8 1 −5 2 −4 3 −5 4 −8 5 −13 What is the average rate of change over the interval [1,5] ? What does the average rate of change indicate? (1 point) Responses The average rate of change is −2 . On average, the y-values of the quadratic function decrease by 2 for every increase of 1 of the x-values over the interval [1,5] . The average rate of change is negative 2 . On average, the y -values of the quadratic function decrease by 2 for every increase of 1 of the x -values over the interval left bracket 1 comma 5 right bracket . The average rate of change is 2. On average, the y-values of the quadratic function decrease by 2 for every increase of 1 of the x-values over the interval [1,5] . The average rate of change is 2. On average, the y -values of the quadratic function decrease by 2 for every increase of 1 of the x -values over the interval left bracket 1 comma 5 right bracket . The average rate of change is 2. On average, the y-values of the quadratic function increase by 2 for every increase of 1 of the x-values over the interval [1,5] . The average rate of change is 2. On average, the y -values of the quadratic function increase by 2 for every increase of 1 of the x -values over the interval left bracket 1 comma 5 right bracket . The average rate of change is −2 . On average, the y-values of the quadratic function increase by 2 for every increase of 1 of the x-values over the interval [1,5] . The average rate of change is negative 2 . On average, the y -values of the quadratic function increase by 2 for every increase of 1 of the x -values over the interval left bracket 1 comma 5 right bracket . Skip to navigation

Answer 1

To calculate the average rate of change of the function \( f(x) \) over the interval \([1, 5]\), we use the formula:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

where \( a = 1 \) and \( b = 5 \).

From the table:
- \( f(1) = -5 \)
- \( f(5) = -13 \)

Plugging the values into the formula:

\[
\text{Average Rate of Change} = \frac{f(5) - f(1)}{5 - 1} = \frac{-13 - (-5)}{5 - 1} = \frac{-13 + 5}{4} = \frac{-8}{4} = -2
\]

So, the average rate of change over the interval \([1, 5]\) is \(-2\).

### Interpretation
The average rate of change of \(-2\) indicates that, on average, the \( y \)-values of the quadratic function decrease by \( 2 \) for every increase of \( 1 \) in the \( x \)-values over the interval \([1, 5]\).

### Correct Response
The average rate of change is −2. On average, the y-values of the quadratic function decrease by 2 for every increase of 1 of the x-values over the interval \([1, 5]\).