Question

The table defines a quadratic function. (Look at the picture below)

What is the average rate of change between x = -1 and x = 1?

The answer is C, but please answer the following questions.

1. List all needed information from the problem.

2. Restate the question in your own words, what is it asking you to find (not just x)? (give me another name for average rate of change)

3. What formulas and/or operations do you need to solve this problem? (Is it on the EOC formula sheet?)

4. Explain what your variables and values are (if necessary)

5. Work out the problems, using numbers and operations and explaining (in words) all steps (include the words "why" and "because", properties)

6. Write your final answer in a sentence, restating the question.

7. Why does your answer make sense? This is a good step to show how you checked your work.

Answer 1

see the explanation

Explanation:

we know that

To find the average rate of change or slope, we divide the change in the output value by the change in the input value

The output value is the variable y

The input value is the variable x

the average rate of change using the data in the table is equal to

`(f(b)-f(a))/(b-a)`

In this problem we have

`a=-1`

`b=1`

`f(a)=f(-1)=5` ---> see the table

`f(b)=f(1)=-1` ----> see he table

Substitute

`(-1-5)/(1+1)=-3`

Remember that slope means "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

In the interval x=-1 and x=1 the average rate is -3

This negative value make sense, because in the interval [-1,1] the function is a decreasing function

so

As the value of x increases, the value of y decreases

As the value of x increases 1 unit to the right the value of y decreases 3 units down