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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 2, Problem 4CT

To determine

To calculate: To explain why a quadratic function models the data. Further, use a linear system to find the model.

Expert Solution & Answer

Answer to Problem 4CT

The equation of the parabola is y=−x2−12x+5 .

Explanation of Solution

Given information: Following data is given,

x	y
2	0
4	-13
6	-34
8	-63
10	-100

Formula used: nth function models the data if nth difference of the model is constant.

Calculation:

Find the first and second differences,

x	y	First difference	Second difference
2	0
4	-13	−13−0=−13
6	-34	−34−(−13)=−34+13=−21	−21−(−13)=−21+13=−8
8	-63	−63−(−34)=−63+34=−29	−29−(−21)=−29+21=−8
10	-100	−100−(−63)=−100+63=−37	−37−(−29)=−37+29=−8

Clearly, it can be observed that the second differences are constant and therefore the quadratic function models the data.

That is, the data can be modeled by the equation,

y=ax2+bx+c

Since three unknowns are to be determined, substitute three values from the model data and simplify for a, b and c

y=ax2+bx+c0=a(2)2+b(2)+c (x=2,y=0)4a+2b+c=0 ...... (1)−13=a(4)2+b(4)+c (x=4,y=−13)16a+4b+c=−13 ...... (2)−34=a(6)2+b(6)+c (x=6,y=−34)36a+6b+c=−34 ...... (3)

On simplifying equations (1), (2) and (3),

a=−1b=−12c=5

Hence, the quadratic equation that models the data is,

y=−x2−12x+5

Chapter 2, Problem 3CT

Chapter 2, Problem 5CT

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

Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - Prob. 51E Ch. 2.1 - Prob. 52E Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - 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