What are the amplitude period phase shift and midline for F(x)=-4cos(3x-3.14)+2

Step-by-step explanation:

f(x) = -4cos(3x-pi) +2

compare to f(x) = A cos (B(x+C))+D

A is amplitude =4

Period is 2pi/B so period = 2pi/3

Phase shift is C so phase shift = -pi (this could be positive if it shifted to the left)

Midline is at D so midline is y=2

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

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.