consider the graph of the quadratic function. which interval
on the x-axis has a negative rate of change?

Option D. 1 to 2.5

Step-by-step explanation:

The complete question is

Consider the graph of the quadratic function. Which interval on the x-axis has a negative rate of change?

Options:

A. –2 to –1

B. –1.5 to 0

C. 0 to 1

D. 1 to 2.5

see the  attached figure to better understand the problem  

we know that

The quadratic function in the graph represent a parabola open downward

The vertex represent a maximum

The x-coordinate of the vertex is approximately 0.5

The axis of symmetry is x=0.5

The function is increasing for x < 0.5 interval (-∞,0.5)

The function is decreasing for x > 0.5 interval (0.5,∞)

Remember that

If the function is decreasing, the rate of change is negative

If the function is increasing, the rate of change is positive

so

The rate of change is negative in the interval (0.5,∞)

therefore

Option A. –2 to –1 ----> rate of change is positive

Option B. –1.5 to 0 ---->  rate of change is positive

Option C. 0 to 1 ---> (0,0.5) the rate of change is positive and (0.5,1) the rate of change is negative

Option D. 1 to 2.5 ---> the rate of change is negative

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.