URGENT! What is the equation of this graph? It is a cosine graph whose equation will fit into terms of y=acos(b(x-c))+d

y=-5cos(pi/8(x+2))-21

Step-by-step explanation:

y=acos(b(x-c))+d

Let's find the max and then the min first. We are aiming to find the amplitude, a, which is the half the distance from the max to the min.

Max is y=-16

Min is y=-26

a=(-16--26)/2=-8--13=5

a could also tell us if y=cos(x) has been reflected about the x-axis if it is -5, which it looks like it has considering cos(0)=1 not -1.

I'm looking at the point (-2,-26) which is the lowest point of our curve and comparing it to our high point of (0,1) on y=cos(x).

So far we have, y=-5cos(b(x-c))+d.

Let's look at d, vertical shift. The average of our max and min is (-26+-16)/2=-13-8=-21.

So our vertical shift is d=-21.

So now equation is y=-5cos(b(x-c))+-21.

Now since we are using (-2,-26) as our (0,1) point on y=cos(x) then c=-2.

So now equation is y=-5cos(b(x--2))+-21

Now we are going to plug in a point haven't mentioned to find b. So looking at graph I will use (6,-16).

-16=-5cos(b(6--2))+-21

Add 21 on both sides:

5=-5cos(b(6--2))

Divide both sides by -5:

-1=cos(b(6--2))

Simplify inside:

-1=cos(b8)

Multiplication is commutative:

-1=cos(8b)

8b=pi * cos(pi)=-1

b=pi/8

The equation is

y=-5cos(pi/8(x--2))+-21

Simplify:

y=-5cos(pi/8(x+2))-21

it would open into a square depending on the type of envelope i’m not sure about the second part