What is the function written in vertex form? f(x) = 5(x + 4) – 80 f(x) = 5(x + 8) – 80 f(x) = 5(x + 4)2 – 80 f(x) = 5(x + 8)2 –
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The first and second coordinate points of the sine graph are;
(0, 20) and (2, 22)
<h3>Sine Graph expression</h3>
The general formula we will use to plot the graph is;
y = [Asin (2πx/t)] + ∅ (Note that sin is in radians)
where;
A is amplitude
t is period
∅ is phase shift
We are told that the buoy bobs up and then down 2 meters from the ocean's depth. This means that;
Amplitude; A = 2
Now, Four seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Thus;
Period = 2 * 4 = 8 seconds
Assume at x = 0, the buoy is at normal ocean depth. Thus;
Phase shift; ∅ = 20
Thus, we have;
y = [2sin((2πx/8)] + 20
At x = 0, we have;
y = [2sin((2π*0/8)] + 20
y = 0 + 20
y = 20
Thus, first point is; (0, 20)
Since the second point must be a maximum or minimum value on the graph closest to the first point, then we put 2 for x to get the coordinate of the second point;
y = [2sin((2π*2/8)] + 20
y = [2sin((2π*2/8)] + 20
y = [2sin(π/2)] + 20
In radians, sin(π/2) = 1. Thus;
y = (2 * 1) + 20
y = 22
Second point is (2, 22)
Using the first and second point coordinates, we will use sine tool to graph the function as attached below.
Read more about sine graph at; brainly.com/question/18055768
