Chapters 6 and 7 - Quadratic Functions Applications

Chapters 6 and 7 - Quadratic Functions – Applications

1. An arrow is fired upward into the air with an initial velocity of 128 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function a) What is the initial height of the arrow? b) What is the height of the arrow 3 seconds later? c) When will the arrow be at a height of 240 feet? d) When does it hit the ground? e) When does it reach the maximum height? f) Find the maximum height of the arrow. g) Graph. Label axes with words and units. Label important information in the graph. 2. An object is thrown upward from the top of a building with an initial velocity of 48 feet per second. The height h(t) (in feet) after t seconds is given by h( t )= - 16 t2 + 48 t + 160 a) What is the initial height of the object? b) What is the height of the object 4 seconds later? c) When will the object be at a height of 192 feet? d) When does it hit the ground? e) When does it reach the maximum height? f) Find the maximum height of the object. g) Graph. Label axes with words and units. Label important information in the graph. Show algebraic work to answer all questions and check answers with the table feature of the calculator 3. The total lengths of fiber-optic cable that telecom companies have for various years are shown in the table. Total Length of Fiber Optic Cable that Telcom Companies Have Year Total length of cable (millions of miles) 1996 21 1997 24 1998 31 1999 42 2000 60 2001 72 Let d= Q( t ) be the total length of cable (in millions of miles) that the telecom companies have at t years since 1996. a. Use the graphing calculator to draw the scatter diagram. What model fits the data well?

3 b. A quadratic model of the situation is Q( t )= t2 + 3 t + 20 . Does the model fit the data well? 2 Use quadratic regression in the calculator to check this model out.

c. An exponential model is E( t )= 19.48(1.3)t . Does this model fit the data well? Use exponential regression in the calculator to check this model out.

d. Use each of the models to predict the total length of cable that the telecom companies will have in 2010. Show work.

e. Solve Q( t )= 32 and E(t) = 32. Show algebraic work. What does it mean in this situation?  After the semester is over, you discover that the math department has changed textbooks (again) so the bookstore won't buy back your nearly-new book. You and your friend Herman decide to get creative. You go to the roof of a twelve-story building and look over the edge to the reflecting pool 160 feet below. You drop your book over the edge at the same instant that Herman chucks his book straight down at 48 feet per second. By how many seconds does his book beat yours into the water?

Our initial launch heights will be the same: we're both launching from 160 feet above ground. And the gravity number, since we're working in feet, will be 16. My initial velocity is zero, since I just dropped my book, but my buddy Herman's velocity is a negative 48, the negative coming from the fact that he chucked his book down rather than up. So our "height" equations are:

mine: s(t) = –16t2 + 160 his: s(t) = –16t2 – 48t + 160