1.10 Modeling with Functions

FILL IN THE BLANKS. This shape of graph is called a _______ because this function is ________. #21

How do I find…

The starting point of an object that is dropped? #6

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. What is the height of the cliff? #27

How do I find…

When an object hits the ground? #8

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. When does the rock hit the ground? #28

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

How many seconds does it take the ball to reach its maximum height? #5

The height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function $$f\left(t\right)=-16t^2+48t$$   , where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height in feet. What is the maximum height the rocket reaches? #2

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p= -15x² +600x +60

What is the maximum profit you can make from selling tickets? #3

How do I find…

How long an object is in the air? #7

A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle? #15

The length of a rectangle is 3 times its width. If the width is increased by 2 cm and the length is increased by 4 cm, its area will be doubled. Find the original dimensions of the rectangle. #26

The area of a playground is 336 yd². The width of the playground is 5 yds. longer than its length. Find the length and width of the playground. #17

A contractor needs 54 square feet of brick to construct a rectangular walkway. The length of the walkway is 15 feet more than the width. Write an equation that could be used to determine the dimensions of the walkway. #32

The length of a rectangle is 4 cm more than its width. The area of the rectangle is 96 sq. cm. Find its dimensions. #34