Math | Graded Assignment | Checkup: Applications of Quadratic Equations Name: Date: Graded Assignment Checkup: Applications of Quadratic Equations Answer the following questions using what you've learned from this lesson. Write your responses in the space provided, and turn the assignment in to your instructor. Problems 1-5: A handy man knows from experience that his 29-foot ladder rests in its most stable position when the distance of its base from a wall is 1 foot farther than the height it reaches up the wall. 1. Draw a diagram to represent this situation. Be sure to label all unknown values in the problem. 2. Write an equation that you can use to find the unknown lengths in this situation. This equation should come directly from the labels you used in your diagram. 3. How far up a wall does this ladder reach? Show your work. © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 1 of 4 Math | Graded Assignment | Checkup: Applications of Quadratic Equations 4. How far should the base be from the wall? Show your work. 5. If the man needs to reach a window 25 feet high on the wall, how far from the wall should he place the base of the ladder? Problems 6-9: Stanford University's soccer field has an area of 8800 square yards. Its length is 30 yards longer than its width. 6. Draw a diagram to represent the soccer field. Include labels of the unknown values in the problem. 7. Write an expression for each dimension (length and width) of the soccer field. 8. Write an equation and solve for the dimensions of the soccer field. © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 2 of 4 Math | Graded Assignment | Checkup: Applications of Quadratic Equations 9. Suppose a new groundskeeper decides that he has enough chalk to line 600 feet of the perimeter of the field. What is the maximum area of the field this chalk could outline, assuming the length remains 30 yards longer than the width? Problems 10-13: A stranded soldier shoots a signal flare into the air to attract the attention of a nearby plane. The flare has an initial vertical velocity of 1500 feet per second. Its height is defined by the quadratic function below. Assume that the flare is fired from ground level. h  v i t  16t 2 10. What is the maximum height that the flare reaches? Show your work. 11. When will the flare reach that height? Show your work. 12. At what time does the flare hit the ground again? Show your work. 13. If the plane is flying at a height of 30,000 feet, a speed of 880 feet per second, and is 50,000 feet from the flare when it is fired, will the flare hit it? If so, tell when this will happen. If not, tell when the flare reaches the plane’s altitude. © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 3 of 4 Math | Graded Assignment | Checkup: Applications of Quadratic Equations Problems 14-17: A farmer has 120 feet of fencing available to build a rectangular pen for her pygmy goats. She wants to give them as much room as possible to run. What are the dimensions of the rectangular pen with the largest area? 14. Draw a diagram to represent this problem. 15. Write an expression in terms of a single variable that would represent the area of a rectangle in this family. 16. Find the dimensions of the rectangle with maximum area. 17. What is another name for this kind of rectangle? © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 4 of 4
Purchase answer to see full attachment