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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Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Question

Chapter 2.3, Problem 43E

To determine

To calculate:The vertex, focus, directrix and the axis of symmetryof the given parabolaand compare the given parabola with its standard equation with p =1 and vertex (0, 0).

Expert Solution & Answer

Explanation of Solution

Given information:The equation of parabola is x=116(y−3)2+1 .

Formula used:

The parabola of the form (x−h)2=4p(y−k), is a vertical parabola

The parabola of the form (y−k)2=4p(x−h), is a horizontal parabola

Calculation:

The equation of given parabola can be written as

(x−1)=116(y−3)2(y−3)2=16(x−1) .....(1)

Which is of the form (y−k)2=4p(x−h) ........(2), therefore it is horizontal parabola.

By comparing equation (1) & (2)

(h,k)=(1,3) & 4p=16 .

Therefore the vertex is (h,k)=(1,3) .

Also,

4p=16p=4

Since p is positive that means the parabola opens right.

Then focus is (h+p,k)=(5,3) .

The directrix is at − p distance from the vertex and here the directrix is a vertical line that passes from (h−p,k)=(−3,3) , therefore the equation of directrixis x=−3 .

The axis of symmetry is the line that passes from the vertex (h,k)=(1,3) and the focus (h+p,k)=(5,3) .therefore the axis of symmetry is y=3 .

The standard equation of this parabola is (y−k)2=4p(x−h) , put p =1 and vertex (0,0)

Then the equation is y2=4x ........(3)

By comparing (1) and (3), it can be observed that

Vertex is shifted from (0,0) to (1,3)

Focus is shifted from (1,0) to (5,3)

Directrix is shifted from x=−1 to x=−3

Axis of symmetry is shifted from y=0 to y=3

Chapter 2.3, Problem 42E

Chapter 2.3, Problem 44E

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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