1.10 Modeling with Functions

​1.10 Modeling with Functions

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Multiple Choice

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

• quadratic; parabola

• parabola; quadratic

• curve; exponential

• line; linear

Multiple Choice

How do I find…

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

• Find the x-value using the axis of symmetry

• Find the axis of symmetry and substitute it into the equation

• Find the y-intercept

• Find the x-intercepts and choose positive value

Multiple Choice

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

• 1.094 ft

• 174.141 ft

• 155 ft

• 4.393 ft

• None of the above

Multiple Choice

How do I find…

When an object hits the ground? #8

• Find the x-value using the axis of symmetry

• Find the axis of symmetry and substitute it into the equation

• Find the y-intercept

• Find the x-intercepts and choose positive value

Multiple Choice

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

• 1.094 seconds

• 174.141 seconds

• 155 seconds

• 4.393 seconds

• None of the above

Multiple Choice

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

• 1.25 seconds

• 1.4 seconds

• 2.5 seconds

• 2 seconds

Multiple Choice

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

• 16 ft

• 36 ft

• 48 ft

• 144 ft

Multiple Choice

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

• $6060

• $20

• $600

• $10,250

Multiple Choice

How do I find…

How long an object is in the air? #7

• Find the x-value using the axis of symmetry

• Find the axis of symmetry and substitute it into the equation

• Find the y-intercept

• Find the x-intercepts and choose positive value

Multiple Choice

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

• 6
• 8
• 3
• 19

Multiple Choice

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

• 7cm by 21cm

• 6cm by 18cm

• 5cm by 15cm

• 4cm by 12cm

Multiple Choice

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

•  length = 26 yd, width = 21 yd
• length = 21 yd, width = 26 yd 
• length = 21 yd, width = 16 yd 
• length = 16 yd, width = 21 yd

Multiple Choice

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

• $$w+\left(w+15\right)=54$$

• $$w\left(w+15\right)=54$$

• $$w\left(w-15\right)=54$$

• $$w^2+\left(w+15\right)^2=54$$

Multiple Choice

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

• 4 cm by 8 cm

• 6 cm by 10 cm

• 8 cm by 12 cm

• 10 cm by 14 cm