Standard Equation for trig function: y = A cos (B (x - H))+ K
*Here, we are just dealing with A (amplitude) and B (period)
Period = 2π/ b
8 = 2π/ b
Solve for b: 2π/8 or π/4
Equation: y = 2 cos (π/4 (x))
Hey there :)
To find the slope with <em>two points</em> we will need to use the equation 

( 3 , -20 ) ( 5 , 8 )
Here is what the equation should look like when replaced with the numbers (<em>it will be a fraction</em>) :

We know that <em>two negatives</em> cancel out and make a positive, so the numerator would actually be 8 + 20.
Solve the fraction and we get 
28 <em>divided</em> by 2 is 14. The slope is 14.
slope intercept form
y=mx+b
where m is the slope and b is the y intercept
if we change from point slope form
y-y1 = m(x-x1)
we distribute
y-y1 = mx -x*x1
then add y1 to each side
y = mx -x*x1+y1
remember x and y are variables and should stay in the equation
m,x1,y1 are numbers from the problem
you may have to calculate the slope (m) from the formula
m = (y2-y1)/(x2-x1) from two points on the line
Answer:
y=3(x+1)^2+7
Step-by-step explanation: