integrated math 3 -3.pdf - Chapter 9 Note If you decided to...

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Unformatted text preview: Chapter 9 Note: If you decided to use the sine function for this situation, you must realize that the aph is shifted to the right %E units. One equation that gives this graph is y = 5 sin [_5L (x— all) + 5 . There are other equations that work, so if you do not get the same equation as shown here, graph yours and compare. To calculate the height of the halloon after Vicki rides 42 inches, y ___ __5 cos [% . 421+ 5 substitute 42 for x in the equation. z —5 cos(8.4) + 5 If you do not get this answer, make sure your = 7.596 inches calculator is in radian mode! Problems State the amplitude and period of each function graphed below. 1. 5. y = 2cos(3x) + 7 6. y = 21— sin(x)— 6 7. fix) = —3sin(4x) 8. y = sin [§ x] + 3 .5 9. fix) = —cos(x) + 27: 10. f(x) = 5 cos(x—1)—% Parent Guide with Extra Practice © 2015 CPM Educational Program. All rights reserved. 107 Sketch the graphs of each of the following functions by hand. Use a graphing calculator to check your answer. 11. 13. 15. 16. 17. 108 y = —2sin(x + 7:) 12. f(x) = %sin(3x) f(x)=cos(4(x—%)) 14. y=3cos(x+%)+3 f(x)= 7sin(]:x)— 3 A wooden water wheel makes ten revolutions every minute. At its lowest point it dips down 2 feet below the surface of the water and at its highest point it is 18 feet above the water. A snail attaches to the edge of the wheel when the wheel is at its lowest point and rides the wheel as it goes around. Use this information to write an equation that gives the height of the snail over time. To keep baby Cristina entertained, her mother often puts her in a Baby Jump Up. It is a seat on the end of a strong spring that attaches in a doorway. When her mom puts Cristina in, she notices that the seat drops to just 8 inches above the floor. Cristina starts to jump and 1.5 seconds later, the seat reaches its highest point of 20 inches above the ground. The seat continues to bounce up and down as time passes. Use this information to write the an equation that gives the height of Cristina’s Baby Jump Up seat over time. (Note: You can start the graph at the point where the seat is at its lowest point.) © 2015 CPM Educational Program. All rights reserved. Core Connections Integrated III Problems For each quadratic function below, describe the transformation, sketch the graph, and state the vertex. 1. y=~2(x—5)2+4 2. y='(x—2)2—5 3. y=(x+3)2—2 4. y=%(x—6)+2 For each situation, write an equation that will model the situation. 5. Twinkle Toes Tony kicked a football, and it landed 100 feet from where he kicked it. It also reached a maximum height of 125 feet. Write an equation that models the path of the ball While it was in the air. 6. When some software companies develop software, they do it with “planned obsolescence” in mind. This means that they plan on the sale of the software to rise, hit a point of maximum sales, then drop and eventually stop when they release a newer version of the software. 'Suppose a graph of the curve showing the number of sales over time can be modeled with a parabola and that the company plans on the “life span” of its product to be 6 months, with maximum sales reaching 1.5 million units. Write an equation that models this situation. 7. A new skateboarder’s ramp just arrived at Bungey’s Family Fun Center. A cross-sectional view shows that the shape is parabolic. The sides are 12 feet high and 15 feet apart. Write an equation that models the cross section of this ramp. Answers 1. my _____________ _ 5. Placing the start of the kick at the origin gives an equation of y =‘ —Q.05x(x — 100). ‘ t _ a». ,. .....,. n...“ -.-w 6. Let the x—axis be the number of months, and the y—axis be the number of ales in millions. Placing the origin at the beginning of sales, gives an equation of y = — % (x — 3)2 +1.5 . 7. Placing the lowest point of the ramp at the origin gives y = 54—22% x2 . Parent Guide and Extra Practice © 2015 CPM Educational Program. All rights reserved. 17 ...
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