These tables represent a quadratic function with a vertex at (0,3) What us the average rate of change from the interval from x=7 to x=8?

The rate of change is shown to the right of the second graph as being -2

At 5 to 6 the average rate of change is -11, so at 6 to 7 the rate of change would be -11-2 = -13, then from 7 to 8 it would be -13-2 = -15.

The answer is D. -15

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PallaviB PallaviB · Answer 2 · 2022-06-30T20:54:27+02:00

The average rate of change from the interval from [tex]x=7[/tex] to [tex]x=8[/tex] will be [tex]-15[/tex] .

What is average rate of change ?

Average rate of change is a measure of how much the function changed per unit, on average, over that interval.

We have,

[tex]x=7[/tex] to [tex]x=8[/tex]

And,

Average rate of change of interval [tex]0[/tex] to [tex]1[/tex] [tex]= -1[/tex]

Average rate of change of interval [tex]1[/tex] to [tex]2[/tex] [tex]= -3[/tex]

Average rate of change of interval [tex]2[/tex] to [tex]3[/tex] [tex]= -5[/tex]

Average rate of change of interval [tex]3[/tex] to [tex]4[/tex] [tex]= -7[/tex]

Average rate of change of interval [tex]4[/tex] to [tex]5[/tex] [tex]= -9[/tex]

Average rate of change of interval [tex]5[/tex] to [tex]6[/tex] [tex]= -11[/tex]

So, from above we can see that there is a difference of [tex]-2[/tex] in Average rate of change in every interval,

So,

Average rate of change of interval [tex]6[/tex] to [tex]7[/tex] [tex]= -13[/tex]

Similarly,

Average rate of change of interval [tex]7[/tex] to [tex]8[/tex] [tex]= -15[/tex]

Hence, we can say that the average rate of change from the interval from [tex]x=7[/tex] to [tex]x=8[/tex] will be [tex]-15[/tex] .

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