Question 1152696
How to find the sinusoidal equation given the maximum and minimum points?

use general formula:

{{{y = A sin (b(x - h)) + k}}}

since max at ({{{3/2}}},{{{12}}}) and  min at ({{{9/2}}},{{{4}}})
we have

{{{k=abs(max - min)}}}

{{{k=12-4=8}}}


{{{A = abs(max-min)/2=(12-4)/2=4}}}

sin periodicity is {{{P=2pi}}} => {{{P/3=(2pi)/3}}},{{{h=0}}}

your function is:

{{{y = 4sin ((2pi/3)x ) + 8}}}


answer: A. {{{y = 4sin ((P/3)x ) + 8}}}



{{{graph( 600, 600, -5, 5, -5, 15, 4sin((2pi/3)x ) + 8) }}}