Question

Let f (x) = -1/2(x + 2)+ 5

-3 to x=1?
What is the average rate of change for the quadratic function from x=-3 to x=1

Answer 1

Rate of change = -1

Explanation:

Given:

f(x) = -½(x + 2)² + 5

Required:

Average rate of change from x = -3 to x = 1

Solution:

Rate of change =
`(f(b) - f(a))/(b - a)`

Where,

a = -3,

f(a) = f(-3) = -½(-3 + 2)² + 5 = -½(-1)² + 5 = 4.5

b = 1,

f(b) = f(1) = -½(1 + 2)² + 5 = -½(9) + 5 = 0.5

Plug in the values into the formula:

Rate of change =
`(0.5 - 4.5)/(1 - (-3))`

Rate of change =
`(-4)/(4)`

Rate of change = -1