Graph a sine function whose amplitude is 5, period is 6π , midline is y=−2 , and y-intercept is (0, −2) . The graph is not a reflection of the parent function over the x-axis.

Question

Graph a sine function whose amplitude is 5, period is  6π , midline is  y=−2 , and y-intercept is (0, −2) . The graph is not a reflection of the parent function over the x-axis.

im not so sure how i would graph this :/

Reiny · Answer

start with
y = 5sin (?x)

period = 2π/k
6π = 2π/k
6πk = 2π
k = 1/3
so far: y = 5 sin ( (1/3)x )

midline is y=−2 , so we have to drop our curve down by 2 units
so far: y = 5 sin ( (1/3)x ) - 2

Testing this for x = 0
y = 5(0) - 2 = -2

y = 5sin (x/3) - 2 will do it

check:
http://www.wolframalpha.com/input/?i=y+%3D+5sin(x%2F3)+-+2+,+y+%3D+-2,+for+0+%E2%89%A4+x+%E2%89%A4+26