how do i solve this?

Question

The curve above is the graph of a sinusoidal function. It goes through the points (-7,0) and (3,0). Find a sinusoidal function that matches the given graph. If needed, you can enter π=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.

Answer 1

(-7,0), (3,0) are points on a sine or cosine wave

= the x intercepts, zeros or roots

general formula is AsinB(x-C)+D

A = Amplitude= (max-min)/2

B = 2pi/period

C = phase (horixontal) shift

D= midline = (max+min)/2 (vertical shift)

without seeing the graph, the most simple equation

has D=0, A=1, C=3

B=2pi/(3+7)= pi/5

y= sin[(pi/5)(x-3)]

or

f(x)= sin(pix/5 -3pi/5)

depending on the graph

transform the equation by a

stretch or compress it by factor of A

and shift up or down by D units

you could also do the same using a cosine instead of sine

with a different phase shift, a different C value,

but A, B, and D would be the same