Question

These tables represent a quadratic function with a vertex at (0,3). What is the
average rate of change for the interval from x = 8 to x = 9?
Interval
х
0
1
2
3
4
5
ilm
у
3
2
-1
-6
-13
-22
--33
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
Average rate
of change
-1
3-2
-3
1-2
-5
1-2
-7
1-2
-9
1-2
-11
6
O A. -78
O B. -61
C.-2
O D. -17

Answer 1

Answer:

These tables represent a quadratic function with a vertex at (0,3). What is the

average rate of change for the interval from x = 8 to x = 9?

Interval

х

0

1

2

3

4

5

ilm

у

3

2

-1

-6

-13

-22

--33

0 to 1

1 to 2

2 to 3

3 to 4

4 to 5

5 to 6

Average rate

of change

-1

3-2

-3

1-2

-5

1-2

-7

1-2

-9

1-2

-11

6

O A. -78

O B. -61

C.-2

O D. -17

Answer 2

The average rate of change on the given interval is -17, so the correct option is D.

How to get the average rate of change?

For a function f(x), the average rate of change on an interval (a, b) is given by:

$r = \frac{f(b) - f(a)}{b - a}$

Here we have the table:

x      y

0     3

1      2

2     -1

3     -6

4     -13

5     -22

Using that data we can find the equation of the parabola.

Because of the first point, we know that:

y = a*x^2 + b*x + 3

Using the second and third pairs, we can write:

2 = a + b + 3

-1 = a*2^2 + b*2 + 3

Then we can solve this sytem of equations, if we simplify the equations we get:

a + b = -1

4a + 2b = -4

To solve this, we need to isolate one of the variables, I will isolate a on the first equation:

a = -1 - b

Then we can replace this with the other equation:

4*(-1 - b) + 2b = -4

Now we can solve this for b.

-4 - 4b + 2b = -4

-2b = 0

b = 0

Then:

a = -1 - b = -1 - 0 = -1

Then the quadratic equation is:

y = f(x) = -x^2 + 3

Now, we need to get:

f(8) = -(8)^2 + 3 = -61

f(9) = -(9)^2 + 3 = -78

Then the average rate of change is:

$r = \frac{-78 - (-61)}{9 - 8} = -17$

So the correct option is D.

If you want to learn more about rates of change, you can read:

https://brainly.com/question/8728504