Download Word Problems

Name _____________________________________
Date ___________________________
Characteristic Word Problem Notes
**When a word problem asks for ________________ or the ____________________ , we should find the __________
**We find the x-value of the _________ by using ___________and the y-value by _________________________
**The x-value is usually (but not always) __________ and the y-value is usually (but not always) _________________
** To see where it is _______________ we find where the graph is going ____________
** To see where it is ______________ we find where the graph is going ____________
** When a problem is on the ground the height is ________
Examples:
1.) Tori jumped off of a cliff into the ocean in Mexico while vacationing with some friends. Her height as a function
of time could be modeled by the function h(t) = -16t2+16t + 380, where t is the time in seconds and h is the
height in feet. When is she at her highest point? What would be her highest point?
2.) Ford makes cars and the formula for cost is C(x) = 2.5x2 – 10x + 19, where C is the cost in thousands of dollars
and x is the number of cars produced in hundreds. How many cars do they need to produce the have the lowest
cost? What would the lowest cost be?
Using the graph to the right, which depicts when a
projectile is shot into the air, answer the following
questions:
a.) At what height is it when it is launched?
b.) How long until it hits the ground?
c.) How long until it is at it’s highest point?
d.) What is it’s highest?
3.)
e.) When is it increasing?
f.) When is it decreasing?
The graph to the left represents the cost of production of
widgets for a company. The y-axis represents cost in
thousands and the x-axis represents number of widgets
produced in hundreds.
a.) What is the cost if no widgets are produced?
b.) What would be the minimum cost possible, and
how many would be produced?
c.) On what interval are you losing money?
d.) On what interval are you making money?
4.)
e.) How many widgets do you have to make/sell to
break even?
Name ________________________________________
Date ___________________________
Characteristic Word Problems
1.) An object is launched directly upward a 64 feet per second from a platform 80 feet high. The formula for it’s height at any
given time is h(t) = –16t2 + 64t + 80. What will be the object’s maximum height?
2.) Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time
could be modeled by the function h(t) = -16t2+16t + 480, where t is the time in seconds and h is the height in feet. How
long did it take for Jason to reach his maximum height? b. What was the highest point that Jason reached?
3.) If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height
h after t seconds is given by the equation h(t)= -16t2+128t. What would be the maximum height and when would it reach it?
4.) You and a friend are hiking in the mountains. You want to climb to a ledge that is 20 ft. above you. The height of the
grappling hook you throw is given by the function h(t) = -16t2 -32t + 5 What is the maximum height of the grappling hook?
Can you throw it high enough to reach the ledge?
5.) You are trying to dunk a basketball. You need to jump 2.5 ft. in the air to dunk the ball. The height that your feet are above
the ground is given by the function h(t) = -16t2 + 12t. What is the maximum height your feet will be above the ground? Will
you be able to dunk the basketball?
6.) Ford makes cars and the formula for cost is C(x) = 3.5x2 – 6x + 17, where C is the cost in dollars and x is the number of cars
produced. How many cars do they need to produce the have the lowest cost?
7.) Gund is makes stuffed Animals and their formula for cost is C(x) = 5.3x2 – 9x + 12, where C is the cost in dollars and x is the
number of stuffed animals produced. What would be the lowest possible cost?
8.) You throw a ball, and it creates the following path. Use the graph to find at what time the ball is going up, and at what time
the ball is coming down. When is it at it’s highest, and at what height? When does it hit the ground?
9.) A rocket is launched. Use the graph to find at what time the rocket is going up, and at what time the rocket is coming down.
When is it at it’s highest, and at what height? When does it hit the ground? How high is it when it is launched?
10.) Your factory produces lemon-scented widgets. You know that each unit is cheaper, the more you produce. But you also
know that costs will eventually go up if you make too many widgets, due to the costs for storage of the overstock. The guy
in accounting says that your cost for producing x thousands of units a day can be approximated by the formula C(x) = 0.04x 2
– 8.50x + 2530. Use the graph below to answer the questions. When does your cost increase and decrease? What is the
lowest possible cost, and how many would you have to produce to have the lowest cost?