These tables represent a quadratic function with a vertex at (0,3). What is the average rate of change for the interval from x = 7 to x = 8?
х
Interval
0
1
2
у
3
2
-1
-6
-13
--22
--33
Average rate
of change
-1
1-2
-3
1-2
-5
1-2
-7
]-2
-9
13-2
-11
O to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
3
4
5
6
O
A. -15
B. -61
C.-2
D. -46

These tables represent a quadratic function with a vertex at (0,-1) what is the average rate of change for the interval from x=7 to x=8?

B.-15

Step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .