Question

Given The partial graph of the cosine function below has a minimum post -2 nd a maximum point at C ) as shown below. The equation of the function can be expressed in the form acos -c))+d. ...c.d w . a) Draw the midline on the graph. b) What is the amplitude of the graph? c) What is the period of the graph? d) What is the value of b in the above equation? e) What is the phase shift in the above graph? f) What is the vertical displacement? g) Write the equation for the above graph in the form y = a cos(b(x - c))+d

Answer 1

y = aws[b(2-0))+d Minimum = (2,-2) Maximum = (1,8) 1070/8) Perund (T1,8) • • Horizontal line that passes exactly between (y=8) and (y=-2) 1.e; y=3. is midline ired colour) Vertical distance between midline and any extremum is ag amplitude . Amplitude = 5 $(8-3) or (3+2) } Distance between two consecutive maximum noints is pernod. i. Period = (TT-o) - Period = π [a= 5 camplitude) Period = 21 = T =) [b= 2 Phase shift = 0 [c=0 Vertical shifl= 3 d =a 2 19 = 50%{ 24'+3]

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