Question

Let e f (x) = x2 – 2x - 4 What is the average rate of change for the quadratic function from X = -1 tox to x = 42 Enter your answer in the box.​

Answer 1

A(x) = 1

Explanation:

`f(-1) = (-1)^(2) -2(-1)-4 == -1\\f(4) = (4)^(2) -2(4)-4 == 4`

When we plug this into the formula for rate of change we end up with...

`(f(4)-f(-1))/(4-(-1)) \\= (4-(-1))/(4+1) \\= (5)/(5)\\= 1`

Answer 2

The average rate of change of the given function

A(x) = 1

Explanation:

Step(i):-

Given function f(x) = x² - 2x -4

And given that x = a = -1 and x=b = 4

The average rate of change of the given function

`A(x) = (f(b)-f(a))/(b-a)`

Step(ii):-

f(x) = x² - 2x -4

f(-1) = (-1)² - 2(-1) -4 = 1+2-4 = -1

f(4) = 4² -2(4) -4 = 16 -12 = 4

The average rate of change of the given function

`A(x) = (f(b)-f(a))/(b-a)`

`A(x) = (4-(-1))/(4-(-1)) = (5)/(5) = 1`

final answer:-

The average rate of change of the given function

A(x) = 1