How do you find period, amplitude, phase shift and midline of #f(x) = −4 sin(2x + π) − 5#?

1 Answer
Ayush S.
Jun 10, 2018

please see below

Explanation:

we have standard form
#asin(bx+c)+-d#
#|a| " is amplitude," (2pi)/|b|" is period," " c is phase shift (or horizontal shift), d is vertical shift"#
comparing the equation with standard form
#a=-4,b=2,c=pi,d=-5#

midline is the line that runs between the maximum and minimum value(#i.e# amplitudes)
since the new amplitude is 4 and graph is shifted 5 units in negative #y-"axis"# (#d=-5#)

therefore maximum value is #4-5=-1# and minimum value is #-4-5=-9# midline will be centre of the region#(-1,-9)" " i.e" "-5 #

phase change =#pi# units right(c is positive)
period is #(2pi)/2=pi#

it will be more clear from graph
graph{-4sin(2x+pi)-5 [-16.02, 16.01, -8.01, 8.01]}

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