Question

These tables represent a quadratic function with a vertex at ( 2, –1). What is the average rate of change for the interval from x = 7 to x = 8?

Answer 1

The average rate of change for the interval from x = 7 to x = 8 is 11 if the function is f(x) = x² - 4x + 3.

What is a quadratic function?

Any function of the form $\rm f(x) =ax^2+bx+c$ where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

We have a table shown in the picture that represents the quadratic function:

As we know,

The quadratic function is in the form:

$\rm f(x) =ax^2+bx+c$

After plugging the points in the above function:

We can find the quadratic function.

4a + 2b + c = -1 ..(1)

9a + 3b + c = 0 ..(2)

9a + 3b + c = 0 ..(3)

After solving three linear equation.

a = 1

b = -4

c = 3

f(x) = x² - 4x + 3

Now,

f(7) = 24

f(8) = 35

The average rate of change for the interval from x = 7 to x = 8:

= (35-24)/(8-7)

= 11

Thus, the average rate of change for the interval from x = 7 to x = 8 is 11 if the function is f(x) = x² - 4x + 3.

Learn more about quadratic function here:

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