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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 xaxis has a negative rate of changeanswersA 2 to 1B 15 to 0C 0 to 1D 1 to 25 class=

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carlosego

The average rate of change is defined as:

[tex] AVR = \frac{f(x2)-f(x1)}{x2-x1} [/tex]

For AVR to be negative, it must comply with:

[tex] x2 - x1> 0
[/tex]

[tex] f (x2) <f (x1)
[/tex]

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;

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

Which gives;

  • [tex]\displaystyle Rate \ of \ change = \frac{\Delta y}{\Delta x} = \mathbf{\frac{y_2 - y_1}{x_2 - x_1}}[/tex]

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;

  • [tex]\displaystyle Rate \ of \ change = \frac{-1 - 3}{2.5 - 1} = \frac{-4}{1.5} = -\frac{8}{3} = \mathbf{-2.\overline 6}[/tex]

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

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

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