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

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)

a

step-by-step explanation:

the denominator cannot be the same as one of the factors.

8 denominator times 2 denominator = 16

and 7 numerator time 11 = 77

77/16= 77/16 ( they cannot be further simplified)