Question

I keep getting this wrong. Please help!

Answer 1

Answer: 6sin( (pi/5)x ) + 1

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Step-by-step explanation:

I'll use the template

y = Asin(kx)+C

where,

• |A| = amplitude
• k = used to find the period
• C = midline

The highest and lowest we can go on the curve is y = 7 and y = -5 respectively. This is a distance of 7 - (-5) = 7 + 5 = 12 units. Half of this vertical distance is the amplitude, so we get 12/2 = 6 as the amplitude. This leads to either A = 6 or A = -6. I'll go with A = 6 for now.

One maximum point is at (-7.5, 7) and its adjacent neighbor max point is (2.5, 7)

This is a horizontal gap of 2.5 - (-7.5) = 2.5+7.5 = 10 units. This is the period of the sine curve because the graph repeats itself every 10 horizontal units along the x axis.

T = period = 10

k = 2pi/T

k = 2pi/10

k = pi/5

The last thing to determine is the value of C. To find this value, find the midpoint of the min and max.

C = (ymin + ymax)/2

C = (-5+7)/2

C = 2/2

C = 1

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To recap, we found these values

• A = 6
• k = pi/5
• C = 1

So we have

y = Asin(kx)+C

update to

y = 6sin( (pi/5)x ) + 1

which is the same as writing
`\text{y} = 6\sin\left((\pi)/(5)\text{x}\right)+1`

You can use a graphing tool such as Desmos or GeoGebra to confirm the answer is correct. Refer to the diagram below.