Question

This table shows values that represent a quadratic function.
0
1
2
3
4
5
6
ㅓ
-2
-5
-10
-17
-26
-37
What is the average rate of change for this
quadratic function for the interval from x = 3
to x = 5?
0-8
0-16
08
016

Answer 1

To find the average rate of change of the quadratic function on the interval from \( x = 3 \) to \( x = 5 \), we use the formula for average rate of change:

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

where \( a \) and \( b \) are the endpoints of the interval.

From the given data, we have:
- \( f(3) = -17 \) (at \( x = 3 \))
- \( f(5) = -37 \) (at \( x = 5 \))

Now, we can substitute these values into the formula:

\[
\text{Average Rate of Change} = \frac{f(5) - f(3)}{5 - 3} = \frac{-37 - (-17)}{5 - 3}
\]

Calculating the numerator:

\[
-37 + 17 = -20
\]

Now, substituting back into the formula gives:

\[
\text{Average Rate of Change} = \frac{-20}{2} = -10
\]

Now, let's look at the choices you provided:

- \( 0 - 8 \)
- \( 0 - 16 \)
- \( 08 \)
- \( 016 \)

None of these options directly match the computed average rate of change of \(-10\).

If you need further clarification or to check the values you provided, let me know!