Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

1st Edition

ISBN: 9781680331165

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 2.4, Problem 33E

To determine

Interpret the meaning of the vertex in this situation.

Expert Solution

Answer to Problem 33E

The vertex is (6,19) shows that the maximum number of students absent from school due to flu is 19 and this happens in day 6.

Explanation of Solution

Given information: The graph shows the number y of students absent from school due to the flu each day x.

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 2.4, Problem 33E , additional homework tip 1

Calculation :

From the graph,

The vertex is (6,19) shows that the maximum number of students absent from school due to flu is 19 and this happens in day 6.

To determine

Write an equation for the parabola to predict the number of students absent on day 10.

Expert Solution

Answer to Problem 33E

The equation of the parabola is f(x)=−0.5(x−6)2+19.

f(10)=11.

Explanation of Solution

Given information: The graph shows the number y of students absent from school due to the flu each day x.

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 2.4, Problem 33E , additional homework tip 2

Calculation :

From the graph,

V(h,k)=(6,19).h=6 and k=19 so the equation of the parabola is, f(x)=a (x−h) 2 +k. f(x)=a (x−6) 2 +16.

Since parabola passes through (0,1).

a (0−6) 2 +19=1.36a+19=1.36a=−18.a=−18/39=−1/2=−0.5 f(x)=−0.5 (x−6) 2 +19. f(10)=−0.5 (10−6) 2 +19.f(10)=−0.5×16+19=−8+19=11.f(10)=11.

To determine

Compare the average rates of change in the students with the flu from 0 to 6 days and 6 to 11 days.

Expert Solution

Answer to Problem 33E

The rate of students getting flu per day was 3 between day 0 and day 6, while from day 6 to day 11 decreased by 2.5 per day.

Explanation of Solution

Given information: The graph shows the number y of students absent from school due to the flu each day x.

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 2.4, Problem 33E , additional homework tip 3

Calculation :

From the graph,

V(h,k)=(6,19).h=6 and k=19 so the equation of the parabola is, f(x)=a (x−h) 2 +k. f(x)=a (x−6) 2 +16.

Since parabola passes through (0,1).

a (0−6) 2 +19=1.36a+19=1.36a=−18.a=−18/39=−1/2=−0.5 f(x)=−0.5 (x−6) 2 +19. f(10)=−0.5 (10−6) 2 +19.f(10)=−0.5×16+19=−8+19=11.

m1=(f(6)−f(0))/(6−0)=(19−1)/6=3.m2=(f(11)−f(6))/(11−6)=(6.5−19)/5=−2.5.

So,

The rate of students getting flu per day was 3 between day 0 and day 6, while from day 6 to day 11 decreased by 2.5 per day.

Chapter 2.4, Problem 32E

Chapter 2.4, Problem 34E

Chapter 2 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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