Determine the equation from the graph says the problem but i dont know how to do this, i saw my notes but still confuse me : (

y = 2·sec((x -3π/2)/2) -4

The general shape of the curve suggests the parent function is a secant or cosecant function. Here, we choose to use the secant. It might help to familiarize yourself with the graph of a secant function (shown in the second attachment).

The centerline between the local maximum and local minimum is at -4, so that is the vertical offset.

The distance between that centerline and a local maximum or minimum is 2 units, so the vertical expansion factor is 2.

The horizontal distance between the local maximum and local minimum is 2π, so represents a horizontal expansion by a factor of 2.

The location of the local minimum is at x=3π/2, so that represents the horizontal offset.

The form of the function with these various transformations is ...

... g(x) = (vertical scale factor) × f((x - (horizontal offset))/(horizontal expansion factor)) - (vertical offset)

Filling in the function and the various values, we get ...

... y = 2·sec((x -3π/2)/2) -4

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.