Trig Equation of a Graph

[Relz]

For my assignment, I was given points to plot then told to connect them with a swooping line. It created a trigonometric function. However, the two "sides"(negative parabola and positive parabola) have different amplitudes. I need to find the equation of this graph in the form f(x) = a sin (kx - c) +d where a, k, c, and d are constants. My guess was f(x) = 6 sin ((x/24) - 9.5) + 27 but when I tested my equation afterwards, it was wrong. I need to get this done ASAP so any help would be greatly appreciated!

Thanks in advance

 

[soroban]

Hello, Relz!

I need the equation of this graph in the form \(\displaystyle f(x) \,=\, a\sin(kx - c) +d\) for constants \(\displaystyle a, k, c, d.\)

My guess was: .\(\displaystyle f(x) \:=\: 6\sin\left(\frac{x}{24}- 9.5\right) + 27\) [COLOR=#e00e] . [/COLOR] . . . Yes, this is wrong.
but when I tested my equation afterwards, it was wrong.


View attachment 1810

It should be: .\(\displaystyle f(x) \;=\;6\sin\left(\dfrac{x-9.5}{12}\pi\right) + 27\)