Question

choose the correct equation(s) for the function shown in the graph. Select all that apply. (There is more than one answer) y = 2cos2(x • π/2) y = -2sin2 x y = -2cos(2 x - π/2) y = 2sin2( x - π/2)

Answer 1

The correct options ares:

b) y = -2sin2x

c) y = -2cos(2 x - π/2)

d) y = 2sin2( x - π/2)

Explanation:

As we can see in the graph, when x = 0 then y = 0.

Simply substitute x=0 in each equation.

a) y = 2cos2(x • π/2)

for (0,0)

y = 2

False

b) y = -2sin2x

for (0,0)

y=0

True

c) y = -2cos(2 x - π/2)

for (0,0)

y=0

True

d) y = 2sin2( x - π/2)

for (0,0)

y=0

True,

(We can also find the solution by using y= Asin(Bx+C) and y = Acos(Bx+C), we'll find that except equation a, all other equations have same amplitude, horizontal shift, period and vertical shift)