Question

given the equation ( y = 6 sin(4(x + 2)) + 3 )
the amplitude is:
the period is:
the horizontal shift is: units to the select an answer
the midline is: ( y = )
add work
check answer

Explanation:

Step1: Find the amplitude

For the general form \(y = A\sin(B(x - C))+D\), the amplitude is \(|A|\).
In \(y = 6\sin(4(x + 2))+3\), \(A = 6\), so amplitude \(=|6| = 6\).

Step2: Find the period

The period formula is \(T=\frac{2\pi}{|B|}\).
Here \(B = 4\), so \(T=\frac{2\pi}{4}=\frac{\pi}{2}\).

Step3: Find the horizontal shift

The horizontal - shift is \(C\) in \(y = A\sin(B(x - C))+D\).
Rewrite \(y = 6\sin(4(x + 2))+3\) as \(y = 6\sin(4(x-(- 2)))+3\), so \(C=-2\), which means a shift of \(2\) units to the left.

Step4: Find the mid - line

The mid - line is \(y = D\).
In \(y = 6\sin(4(x + 2))+3\), \(D = 3\), so mid - line \(y = 3\).

Answer:

Amplitude: \(6\)
Period: \(\frac{\pi}{2}\)
Horizontal shift: \(2\) units to the left
Midline: \(y = 3\)