Answer: A
Step-by-step explanation:
The standard form of a cosine equation is: y = A cos (Bx - C) + D where
- Amplitude (A) is the distance from the center to the max
- Period (P) is the length of the function = 2π/B
- Phase Shift is the distance the max is moved from the y-axis = C/B
- Center (D) is the imaginary line between the max and min
Plot the points (see graph below).
A = 28
[tex]\dfrac{1}{2}P=6\quad \rightarrow \quad P=12\\\\\\P=\dfrac{2\pi}{B}\qquad \rightarrow \qquad 12=\dfrac{2\pi}{B}\qquad \rightarrow \qquad \large\bold{B=\dfrac{\pi}{6}}[/tex]
Phase Shift = 7 = C/B
[tex]7=\dfrac{C}{\frac{\pi}{6}}\qquad \rightarrow \qquad \large\bold{C=\dfrac{7\pi}{6}}[/tex]
D = 49
Input the values of A, B, C, and D into the standard form of a cosine equation to get:
[tex]\large\boxed{y=28\cos \bigg(\dfrac{\pi}{6}x-\dfrac{7\pi}{6}\bigg)+49}[/tex]
