Answer. Second option: y=0.5 cos (4(x+pi/2))-2
Solution:
y=a cos (b(x+c))+d
ymax=-1.5; y min=-2.5
d=(ymax+ymin)/2
d=(-1.5+(-2.5))/2
d=(-1.5-2.5)/2
d=(-4.0)/2
d=-2.0
The horizontal axis is y=-2→d=-2
y= a cos(b(x+c))+(-2)
y=a cos (b(x+c))-2
The amplitude (a) is:
a=ymax-d=d-ymin
a=-1.5-(-2)=-2-(-2.5)
a=-1.5+2=-2+2.5
a=0.5=0.5
The period is Pi/2 because in Pi units the graph repeats twice:
Period: P=Pi/2
P=2Pi/b
Replacing P by Pi/2 in the formula above:
Pi/2=2Pi/b
Solving for b: Multiplying both sides of the equation by 2b:
2b(Pi/2)=2b(2Pi/b)
Pi b=4 Pi
Dividing both sides of the equation by Pi:
(Pi b)/Pi=(4 Pi)/Pi
b=4
y=0.5 cos (4(x+c))-2
We can say that the graph is translated Pi/2 units to the left, then c=Pi/2
y=0.5 cos (4(x+pi/2))-2
