FAN AND MEDAL! What is an approximate average rate of change of the graph from x = 3 to x = 5 for f(x)=-13.333(x - 3)^2+120 ?

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FAN AND MEDAL! What is an approximate average rate of change of the graph from x = 3 to x = 5 for f(x)=-13.333(x - 3)^2+120 ?

Mathematics
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\[\frac{ f(5)-f(3) }{ 5-3 }\]
f(x)=-13.333(x - 3)^2+120 is the equation f(5)=-13.333(x - 5)^2+120 f(5)=-13.333x^2-333.33 @Shalante is this right so far?

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Nope, no need to change the (x-3)
f(x)=-13.333(x - 5)^2+120 is the equation f(5)=-13.333(x - 5)^2+120 f(5)=-13.333x^2-333.33+120 f(5)=-13.333x^2-213.33
Do not change anything besides the x Plug in x=5 and x=3 Subtract f(5)-f(3) Divide it by 2 since that is the interval difference.
so how would i solve it? i need to show the steps
f(x)=-13.333(5 - 3)^2+120 is the equation f(5)=-13.333(2)^2+120 f(5)=-13.333(4)+120 ?
f(5)=-13.333(4)+120 f(5)=-53.33+120 f(5)=66.67 ??
replace x with 5 to get answer #1 replace x with 3 to get answer #2 (answer #1 - answer #2) / 2
@Shalante did i solve it for x=5 correctly tho?
yea f(5) is correct.
ok and then f(x)=-13.333(x - 3)^2+120 f(3)=-13.333(3 - 3)^2+120 f(3)=-13.333(0)+120 f(3)=120 ?
Yes. now subtract it and then divide by 2
66.67-120/2 -53.33/2 -26.67
is that right?
Yes, that is correct.
ok thanks!
what does this rate represent in this situation? The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, being sold by the company:
-26.67 means the slope is decreasing at an average of 26.67 from x=3 to x=5
the rate of the profit they are getting. rate is change of y. y is f(x) f(x) is the profit.
so their profit is decreasing by 66.67?
You mean decreasing by 26.67?
oh yea lol
Yes, from 3 shirts sold to 5 shirts, the profit decreased by an average of $26.67.
ok thanks gtg!!
No problem!

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