# Find Amplitude, Period, and Phase Shift f(x)=-3cos(4x+pi)+6

Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Find the amplitude .
Amplitude:
Find the period using the formula .
The period of the function can be calculated using .
Period:
Replace with in the formula for period.
Period:
Solve the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Period:
Cancel the common factor of and .
Factor out of .
Period:
Cancel the common factors.
Factor out of .
Period:
Cancel the common factor.
Period:
Rewrite the expression.
Period:
Period:
Period:
Period:
Period:
Find the phase shift using the formula .
The phase shift of the function can be calculated from .
Phase Shift:
Replace the values of and in the equation for phase shift.
Phase Shift:
Move the negative in front of the fraction.
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the left)
Vertical Shift:
Find Amplitude, Period, and Phase Shift f(x)=-3cos(4x+pi)+6

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