Question

a sine function has the following key features:
period = 4π
amplitude = 3
midline: y = 2
y-intercept: (0, 2)
the function is a reflection of its parent function over the x-axis.
use the sine tool to graph the function. the first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
graph interface with move, sine, undo, redo, reset buttons and a y-axis with grid lines

Explanation:

Step1: Write general sine function form

General form: $y = A\sin(Bx + C) + D$
Reflection over x-axis: $A = -3$
Midline $D = 2$
Period $4π = \frac{2π}{B} \Rightarrow B = \frac{1}{2}$
y-intercept (0,2): $2 = -3\sin(C) + 2 \Rightarrow \sin(C)=0 \Rightarrow C=0$
Function: $y = -3\sin(\frac{1}{2}x) + 2$

Step2: Find first point (midline)

Midline $y=2$, x=0: $(0,2)$

Step3: Find closest max/min

First min at $\frac{1}{2}x = \frac{π}{2} \Rightarrow x=π$, $y=-3(1)+2=-1$: $(π,-1)$

Answer:

First point: (0, 2); Second point: (π, -1)