G(x) = 2 cos [2x (x+2π/3)] -5 With respect to the parent function F(x) = cos(x) What is the amplitude, period, phase shift, and vertical translation of the function G(x)?

The amplitude is 2

The period is π/x

The phase shift is -2π/3

The vertical translation is -5

Step-by-step explanation:

The equation of the given function is G(x) = 2·cos[2·x·(x + 2π/3)] - 5

Comparing with the general equation for the cosine function, y = d + a·cos(b·(x - c))

Where:

= The amplitude

2·π/b = The period

c = The phase shift

d = Vertical shift

Therefore, we have;

The amplitude = 2

The period = 2·π/(2·x) = π/x

The phase shift = -2π/3 (The sign is opposite to in sign to the sign following it in the parenthesis of the angle of rotation

-5 = The vertical translation of the function G(x)

1.677

step-by-step explanation:

i'm not good at explaining stuff but if you need an answer i'm here for you.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb