a. Answer The required maximum height of the birdie is 20 feet. Explanation Given information: The function: h = − 16 t 2 + 32 t + 4 Calculation: The given function is h = − 16 t 2 + 32 t + 4 . Rewrite the above function in the vertex form f ( x ) = a ( x − h ) 2 + k as: h = − 16 t 2 + 32 t + 4 h = − 16 ( t 2 − 2 t ) + 4 h = − 16 ( t 2 − 2 t + 1 ) + 16 + 4 h = − 16 ( t − 1 ) 2 + 20 The vertex of the above function is ( 1 , 20 ) . The y -coordinate of the above vertex is the maximum height of the birdie that is, 20. Hence, the required maximum height of the birdie is 20 feet. b. To determine To calculate: The time for which the birdie is in the air. Answer The required time for which the birdie is in the air is 2.12 seconds. Explanation Given information: The function: h = − 16 t 2 + 32 t + 4 Calculation: The given function is h = − 16 t 2 + 32 t + 4 . Rewrite the above function in the vertex form f ( x ) = a ( x − h ) 2 + k as: h = − 16 t 2 + 32 t + 4 h = − 16 ( t 2 − 2 t ) + 4 h = − 16 ( t 2 − 2 t + 1 ) + 16 + 4 h = − 16 ( t − 1 ) 2 + 20 To find the required time, solve the above equation for t . − 16 ( t − 1 ) 2 + 20 = 0 − 16 ( t − 1 ) 2 − 16 = − 20 − 16 ( t − 1 ) 2 = 5 4 Take square root on each side of the above expression. ( t − 1 ) 2 = 5 4 t − 1 = ± 5 2 t = 1 ± 5 2 t = 1 ± 1.12 Solve for t . t = 1 + 1.12 t = 2.12 And, t = 1 − 1.12 t = − 0.12 But time cannot be negative. Hence, the required time for which the birdie is in the air is 2.12 seconds.

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

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Question

Chapter 3.3, Problem 18Q

To determine

To calculate: The maximum height of the birdie.

Expert Solution

Answer to Problem 18Q

The required maximum height of the birdie is 20 feet.

Explanation of Solution

Given information:

The function: h=−16t2+32t+4

Calculation:

The given function is h=−16t2+32t+4 .

Rewrite the above function in the vertex form f(x)=a(x−h)2+k as:

h=−16t2+32t+4h=−16(t2−2t)+4h=−16(t2−2t+1)+16+4h=−16(t−1)2+20

The vertex of the above function is (1,20) .

The y -coordinate of the above vertex is the maximum height of the birdie that is, 20.

Hence, the required maximum height of the birdie is 20 feet.

To determine

To calculate: The time for which the birdie is in the air.

Expert Solution

Answer to Problem 18Q

The required time for which the birdie is in the air is 2.12 seconds.

Explanation of Solution

Given information:

The function: h=−16t2+32t+4

Calculation:

The given function is

h=−16t2+32t+4 .

Rewrite the above function in the vertex form f(x)=a(x−h)2+k as:

h=−16t2+32t+4h=−16(t2−2t)+4h=−16(t2−2t+1)+16+4h=−16(t−1)2+20

To find the required time, solve the above equation for t .

−16(t−1)2+20=0−16(t−1)2−16=−20−16(t−1)2=54

Take square root on each side of the above expression.

(t−1)2=54t−1=±52t=1±52t=1±1.12

Solve for t .

t=1+1.12t=2.12

And, t=1−1.12t=−0.12

But time cannot be negative.

Hence, the required time for which the birdie is in the air is 2.12 seconds.

Chapter 3.3, Problem 17Q

Chapter 3.4, Problem 1E

Chapter 3 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

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