Which is the best estimate for the average rate of change for the quadratic function graph on the interval 0 ≤ x ≤ 4?A) −1 B) −2 C) −3 D) −4

ANSWER

A) -1

EXPLANATION

The average rate of change of the given quadratic function on the interval 0 ≤ x ≤4 is the slope of the secant line connecting the points (0,f(0)) and (4,f(4)).

That is the average rate of change is:

[tex] = \frac{f(4) - f(0)}{4 - 0} [/tex]

From the graph, f(0) is 0 and f(4) is -4.

We plug in these values to obtain;

[tex] = \frac{ - 4 - 0}{4 - 0} [/tex]

This simplifies to;

[tex] = \frac{ - 4}{4} [/tex]

[tex] = - 1[/tex]

Hence the average rate of change for the given quadratic function whose graph is shown on 0≤x≤4 is -1