Question

5. Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7. my equation is F(x) = 3 (x-3)^2 + 4 in vertex form and and y = 3x^2 - 18x +31. Any ideas how to do this would be super helpful and I'll give you a medal!

Answer 1

y = 3x^2 - 18x +31 in standard form

Answer 2

use the slope formula... you need 2 points

average rate of change is

\[\frac{f(b) - f(a)}{b - a}\]

so substitute the x values to get a corresponding f(x) then substitute into the formula

Answer 3

How do I do that? Like I know I need a y correct? So do I solve for x plug that in the parabola formula and use the y and find the slope?

Answer 4

of so looking at the equation in vertex form find F(7)

\[F(7) = 3(7 -3)^2 + 4 = 52\]

and for x = 4

\[F(4) = 3(4 -3)^2 + 4 = 7\]

so the average rate of change is

\[\frac{52 - 7}{7 - 4} = \]

same process for the standard form equation.

Answer 5

oops just realised they are the same equations... so all you need to do is simplify the fraction for the average rate of change...

Answer 6

So you plug in the number for x, solve for y then you get that fraction?

Answer 7

you do... you actually get 2 points as shown above (7, 52) and (4, 7)

so all you need to do for the average rate of change is find the slope of the interval joining the 2 points

Answer 8

And how would I do that?

Answer 9

well you you go up to my 1st post you have

(52 - 7)/(7 -4) =

just evaluate it

Answer 10

is it 15?...

Answer 11

thats it... the average rate of change.

Answer 12

So the average rate of change is 15? I feel silly for even asking that question haha... Thank you :)

Answer 13

yes... its the average rate of change in x with respect to y...

glad to help