Aim #65: How do we interpret real world applications of quadratic functions?
(Day 2)
Homework: Handout
Do Now: An acorn falls from the branch of a tree to the ground 25 feet below.
The distance, S, the acorn is from the ground as it falls is represented by the
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equation S(t) = -16t + 25, where t represents time, in seconds. Calculate the time
the acorn will take to reach the ground.
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1) The height of an object, h(t), is determined by the formula h(t) = -16t + 256t,
where t is time, in seconds. Find the maximum height of the object and at what
time the object hits the ground.
2) Paige wants to start a summer lawn-mowing business. She comes up with the
following profit function that relates the total profit to the rate she charges for
a lawn-mowing job:
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P(x) = -x + 40x - 100
a) According to the function, what is her initial cost (e.g., maintaining the mower,
buying gas, advertising)? Explain your answer in the context of this problem.
b) Between what two prices does she have to charge to make a profit? Write
answers in simplest radical form and to the nearest hundredth. c) If she wants to make a $275 profit this summer, is this the right business
choice?
3) Pete and Ray each threw a baseball into the air.
The vertical height of Pete's baseball is represented by the graph P(t) above.
P(t) represents the vertical distance of the baseball from the ground in feet
and t represents time in seconds. The vertical height of Ray's baseball is
represented by the table of values R(t):
R(t) represents the vertical distance of the baseball from the ground in feet
and t represents time in seconds.
a) Whose baseball reached the highest? Explain your answer.
b) Whose ball reached the ground fastest? Explain your answer.
c) Pete claims that his ball reached its maximum faster than Ray‛s? Is his
claim correct or incorrect? Explain your answer.
d) Find P(0) and R(0) values and explain what it means in the problem. What
conclusion can you make based on these values? Did they throw the ball from
the same place? Explain your answer.
e) Ray claims that he can throw the ball higher than Pete. Is his claim
correct or incorrect? Explain your answer.
4) A rocket is launched from a cliff. The relationship between the height,
h, in feet, of the rocket and the time, t, in seconds, since its launch can be
represented by the following function:
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h(t) = -16t + 80t + 384
a) When will the projectile hit the ground?
b) When will the rocket hit the maximum height?
c) What is the maximum height the rocket reaches?
d) At what height was the rocket launched?
5) The height of a baseball h(t) at time t, where t = 0 and where the ball is
struck initially at 4 feet above ground, is modeled by the equation
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h(t) = -16t + 64t + 4. After how many seconds is the ball at a height of
exactly 52 feet?