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Consider the graph of the quadratic function. Which interval on the x-axis has a negative rate of change?
answers:
A. –2 to –1B. –1.5 to 0C. 0 to 1D. 1 to 2.5

Consider the graph of the quadratic function. Which interval on the x-axis has a negative rate of change? answers: A. 2 to 1B. 1.5 to 0C. 0 to 1 D. 1 to 2.5 class=

Verified Answer :

carlosego

The average rate of change is defined as:

\(AVR = \frac{f(x2)-f(x1)}{x2-x1}\)

For AVR to be negative, it must comply with:

\(x2 - x1> 0
\)

\(f (x2) \)

Therefore, we observe that the interval that fulfills these conditions is the whole interval to the right of the parabola.

Among the options given, this interval is:

1 to 2.5

Answer:

An interval on the x-axis that has a negative rate of change is:

D. 1 to 2.5

The rate of change of a graph is positive when the graph is increasing from left to right and it is negative when it is decreasing from left to right

  • The interval on the x-axis that has a negative rate of change is option D. 1 to 2.5.

Reasons:

Rate of change is given by the equation;

  • \(\displaystyle Rate \ of \ change = \mathbf{\frac{Chnage \ in \ (vertical) \ y-value}{Change \ in \ (horizontal) \ x-value}}\)

Which gives;

  • \(\displaystyle Rate \ of \ change = \frac{\Delta y}{\Delta x} = \mathbf{\frac{y_2 - y_1}{x_2 - x_1}}\)

In the range where the graph is decreasing from left to right, we have in the x-axis interval, 1 to 2.5, the points (1, 3), and (2.5, -1)

Therefore;

  • \(\displaystyle Rate \ of \ change = \frac{-1 - 3}{2.5 - 1} = \frac{-4}{1.5} = -\frac{8}{3} = \mathbf{-2.\overline 6}\)

Therefore, the rate of change of the quadratic function in the x-axis interval 1 to 2.5 is \(-2.\overline 6\), which is negative;

  • The interval with a negative rate of change is; 1 to 2.5

Learn more about rate of change of a quadratic function here:

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