11. Constructed Response 1 & 2

Constructed Response 1

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​Watch this animation to help you answer the next question.

Multiple Choice

Page 6a.

This graph models the height of a swinging pirate ship ride at an amusement park.

Use the graph to determine how long it takes the pirate ship to make a full swing back and forth (all the way to the right, all the way to the left and back at the center).

The animation on the slide before can help.

• 4 seconds

• 8 seconds

• 12 seconds

• 6 seconds

• 2 seconds

Open Ended

Page 6b.

Is the time the same as the period of the function? Why or why not?

Multiple Select

Page 6c & d

Using the sine and cosine parent function, find two function rule that models this situation.

Hint: Graph each on Desmos (in radian mode) and figure out which two match.

• $$y=10\sin\left(\frac{\pi}{2}x+1\right)+10$$

• $$y=\sin\left(\frac{\pi}{2}\left(x-1\right)\right)+10$$

• $$y=\sin\left(\frac{\pi}{2}x\right)+10$$

• $$y=-10\cos\left(\frac{\pi}{2}x\right)+10$$

• $$y=\cos\left(\frac{\pi}{2}x\right)+10$$

Constructed Response 2

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​Make these changes on your paper

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​Make these changes on your paper

​Steps to Graph

​x values- how many minutes?

​y values- where does it start?how tall?

Distance to midline from the min or the max

Up and down. Look at where it repeats on the graph

Figure out the max, figure out the min. Add together and divide by 2

​Use this to hel you on the next slide

Labelling

Page 7 #1

Fill in the information from the table.

Drag labels to their correct position on the image

117.5

112.5

[0, 6]

[5, 230]

2 minutes

Multiple Choice

Equation

$$y=a\sin b\left(x-h\right)+k$$

a=amplitude $$\frac{2\pi}{b}=period$$ h= horizontal shift from parent k=midline

• $$y=115.5\sin\left(2x-\frac{\pi}{2}\right)+117.5$$

• $$y=117.5\sin\left(\pi x-\frac{\pi}{2}\right)+112.5$$

• $$y=117.5\sin\left(2x\right)+112.5$$

Labelling

Page 7 #2

Fill in the information from the table

Drag labels to their correct position on the image

Ferris wheel is moving back down

Diameter of the wheel

Ferris wheel is rising

At the top of the Ferris wheel

At the bottom of the Ferris wheel