My Equation:
F(x) = 2(x - 5) ² + 14

Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7.

Question

My Equation:
F(x) = 2(x - 5) ² + 14

Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7.

zasharra · Answer

@campbell_st @amistre64

zasharra · Answer

@Astrophysics do yu know?

astrophysics · Answer

Yes, average rate of change is just $$A(x) = \frac{ f(b)-f(a) }{ b-a }$$ so a = 4 and b = 7

astrophysics · Answer

To find f(b) and f(a) simply plug in 4 and 7 into your functions for x and evaluate

astrophysics · Answer

You should notice something about this formula

zasharra · Answer

F(x) = 2(x - 5) ² + 14

F(x) = 4(x - 5) ² + 14

idk where 7 should go

astrophysics · Answer

$$f(b) = f(7) = 2[(7)-5]^2+14 $$

astrophysics · Answer

Do the same for f(4)

astrophysics · Answer

Once you find the values plug it all into the formula

zasharra · Answer

I really have clue of what to do

campbell_st · Answer

you need to us substitution, 

replacing x with 4 and then calculating a value, this will give F(4)

then repeat the process except use x = 7 to find f(7)

then you have 2 points

(4, F(4)) and (7, F(7))

then find the slope formula to find the average rate of change between two points

zasharra · Answer

How can I sum this up in sentences because that's what the question is asking?

astrophysics · Answer

You have all the information, try to evaluate it first, as campbell mentioned this is the slope formula which is what I was trying to get you to notice.

zasharra · Answer

Thank you two so much. I got it now!! Love you guys!!! XoXoXo