Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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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.

Videos

Question

Chapter 7.5, Problem 11OE

To determine

To determine whether the parabola opens upward or downward.

Expert Solution

Answer to Problem 11OE

Parabola opens downward

Explanation of Solution

Given information :

Given equation y=−3(x−1)2

We know that the graph of the equation y−k=a(x−h)2 opens upwards when a>0 and downwards when a<0 .

The coordinates of the vertex is given by (h,k)

Axis of symmetry is given by the value of h

Now we compare the given equation with the standard equation, we get,

Here the value of a=−1,(a<0) hence the graph of parabola opens downwards.

To determine

The coordinates of the vertex.

Expert Solution

Answer to Problem 11OE

Coordinates of the vertex is (1, 0)

Explanation of Solution

Given information :

Given equation y=−3(x−1)2

We know that the graph of the equation y−k=a(x−h)2 opens upwards when a>0 and downwards when a<0 .

The coordinates of the vertex is given by (h,k)

Axis of symmetry is given by the value of h

Now we compare the given equation with the standard equation, we get,

k=0

And h=1

Therefore the coordinates of the vertex is (1, 0)

To determine

The equation of the axis of symmetry.

Expert Solution

Answer to Problem 11OE

Axis of symmetry is x=1

Explanation of Solution

Given information :

Given equation y=−3(x−1)2

We know that the graph of the equation y−k=a(x−h)2 opens upwards when a>0 and downwards when a<0 .

The coordinates of the vertex is given by (h,k)

Axis of symmetry is given by the value of h

Now we compare the given equation with the standard equation, we get,

h=1

Therefore the coordinates of the vertex is (1, 0)

Axis of symmetry is x=1

Chapter 7.5, Problem 10OE

Chapter 7.5, Problem 12OE

Chapter 7 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 7.1 - Prob. 1OE Ch. 7.1 - Prob. 2OE Ch. 7.1 - Prob. 3OE Ch. 7.1 - Prob. 4OE Ch. 7.1 - Prob. 5OE Ch. 7.1 - Prob. 6OE Ch. 7.1 - Prob. 7OE Ch. 7.1 - Prob. 8OE Ch. 7.1 - Prob. 9OE Ch. 7.1 - Prob. 10OE

Ch. 7.1 - Prob. 11OE Ch. 7.1 - Prob. 12OE Ch. 7.1 - Prob. 13OE Ch. 7.1 - Prob. 14OE Ch. 7.1 - Prob. 15OE Ch. 7.1 - Prob. 16OE Ch. 7.1 - Prob. 17OE Ch. 7.1 - Prob. 18OE Ch. 7.1 - Prob. 19OE Ch. 7.1 - Prob. 20OE Ch. 7.1 - Prob. 1WE Ch. 7.1 - Prob. 2WE Ch. 7.1 - Prob. 3WE Ch. 7.1 - Prob. 4WE Ch. 7.1 - Prob. 5WE Ch. 7.1 - Prob. 6WE Ch. 7.1 - Prob. 7WE Ch. 7.1 - Prob. 8WE Ch. 7.1 - Prob. 9WE Ch. 7.1 - Prob. 10WE Ch. 7.1 - Prob. 11WE Ch. 7.1 - Prob. 12WE Ch. 7.1 - Prob. 13WE Ch. 7.1 - Prob. 14WE Ch. 7.1 - Prob. 15WE Ch. 7.1 - Prob. 16WE Ch. 7.1 - Prob. 17WE Ch. 7.1 - Prob. 18WE Ch. 7.1 - Prob. 19WE Ch. 7.1 - Prob. 20WE Ch. 7.1 - Prob. 21WE Ch. 7.1 - Prob. 22WE Ch. 7.1 - Prob. 23WE Ch. 7.1 - Prob. 24WE Ch. 7.1 - Prob. 25WE Ch. 7.1 - Prob. 26WE Ch. 7.1 - Prob. 27WE Ch. 7.1 - Prob. 28WE Ch. 7.1 - Prob. 29WE Ch. 7.1 - Prob. 30WE Ch. 7.1 - Prob. 31WE Ch. 7.1 - Prob. 32WE Ch. 7.1 - Prob. 33WE Ch. 7.1 - Prob. 34WE Ch. 7.1 - Prob. 35WE Ch. 7.1 - Prob. 36WE Ch. 7.1 - Prob. 37WE Ch. 7.1 - Prob. 38WE Ch. 7.1 - Prob. 39WE Ch. 7.1 - Prob. 40WE Ch. 7.1 - Prob. 41WE Ch. 7.1 - Prob. 42WE Ch. 7.1 - Prob. 1MRE Ch. 7.1 - Prob. 2MRE Ch. 7.1 - Prob. 3MRE Ch. 7.1 - Prob. 4MRE Ch. 7.1 - Prob. 5MRE Ch. 7.1 - Prob. 6MRE Ch. 7.1 - Prob. 7MRE Ch. 7.1 - Prob. 8MRE Ch. 7.1 - Prob. 9MRE Ch. 7.2 - Prob. 1OE Ch. 7.2 - Prob. 2OE Ch. 7.2 - Prob. 3OE Ch. 7.2 - Prob. 4OE Ch. 7.2 - Prob. 5OE Ch. 7.2 - Prob. 6OE Ch. 7.2 - Prob. 1WE Ch. 7.2 - Prob. 2WE Ch. 7.2 - Prob. 3WE Ch. 7.2 - Prob. 4WE Ch. 7.2 - Prob. 5WE Ch. 7.2 - Prob. 6WE Ch. 7.2 - Prob. 7WE Ch. 7.2 - Prob. 8WE Ch. 7.2 - Prob. 9WE Ch. 7.2 - Prob. 10WE Ch. 7.2 - Prob. 11WE Ch. 7.2 - Prob. 12WE Ch. 7.2 - Prob. 13WE Ch. 7.2 - Prob. 14WE Ch. 7.2 - Prob. 15WE Ch. 7.2 - Prob. 16WE Ch. 7.2 - Prob. 17WE Ch. 7.2 - Prob. 18WE Ch. 7.2 - Prob. 19WE Ch. 7.2 - Prob. 20WE Ch. 7.2 - Prob. 21WE Ch. 7.2 - Prob. 22WE Ch. 7.2 - Prob. 23WE Ch. 7.2 - Prob. 24WE Ch. 7.2 - Prob. 25WE Ch. 7.2 - Prob. 26WE Ch. 7.2 - Prob. 27WE Ch. 7.2 - Prob. 28WE Ch. 7.2 - Prob. 29WE Ch. 7.2 - Prob. 30WE Ch. 7.2 - 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Prob. 8WE Ch. 7.3 - Prob. 9WE Ch. 7.3 - Prob. 10WE Ch. 7.3 - Prob. 11WE Ch. 7.3 - Prob. 12WE Ch. 7.3 - Prob. 13WE Ch. 7.3 - Prob. 14WE Ch. 7.3 - Prob. 15WE Ch. 7.3 - Prob. 16WE Ch. 7.3 - Prob. 17WE Ch. 7.3 - Prob. 18WE Ch. 7.3 - Prob. 19WE Ch. 7.3 - Prob. 20WE Ch. 7.3 - Prob. 21WE Ch. 7.3 - Prob. 22WE Ch. 7.3 - Prob. 23WE Ch. 7.3 - Prob. 24WE Ch. 7.3 - Prob. 25WE Ch. 7.3 - Prob. 26WE Ch. 7.3 - Prob. 27WE Ch. 7.3 - Prob. 28WE Ch. 7.3 - Prob. 29WE Ch. 7.3 - Prob. 30WE Ch. 7.3 - Prob. 31WE Ch. 7.3 - Prob. 32WE Ch. 7.3 - Prob. 33WE Ch. 7.3 - Prob. 34WE Ch. 7.3 - Prob. 35WE Ch. 7.3 - Prob. 36WE Ch. 7.3 - Prob. 37WE Ch. 7.3 - Prob. 38WE Ch. 7.3 - Prob. 39WE Ch. 7.3 - Prob. 40WE Ch. 7.3 - Prob. 41WE Ch. 7.3 - Prob. 42WE Ch. 7.3 - Prob. 43WE Ch. 7.3 - Prob. 1MRE Ch. 7.3 - Prob. 2MRE Ch. 7.3 - Prob. 3MRE Ch. 7.3 - Prob. 4MRE Ch. 7.3 - Prob. 5MRE Ch. 7.3 - Prob. 6MRE Ch. 7.3 - Prob. 7MRE Ch. 7.3 - Prob. 8MRE Ch. 7.3 - Prob. 9MRE Ch. 7.3 - Prob. 10MRE Ch. 7.3 - Prob. 11MRE Ch. 7.3 - Prob. 12MRE Ch. 7.3 - Prob. 13MRE Ch. 7.3 - Prob. 14MRE Ch. 7.3 - Prob. 1CE Ch. 7.3 - Prob. 2CE Ch. 7.3 - Prob. 3CE Ch. 7.3 - Prob. 4CE Ch. 7.3 - Prob. 5CE Ch. 7.3 - Prob. 6CE Ch. 7.4 - Prob. 1OE Ch. 7.4 - Prob. 2OE Ch. 7.4 - Prob. 3OE Ch. 7.4 - Prob. 4OE Ch. 7.4 - Prob. 5OE Ch. 7.4 - Prob. 6OE Ch. 7.4 - Prob. 7OE Ch. 7.4 - Prob. 8OE Ch. 7.4 - Prob. 9OE Ch. 7.4 - Prob. 10OE Ch. 7.4 - Prob. 11OE Ch. 7.4 - Prob. 12OE Ch. 7.4 - Prob. 1WE Ch. 7.4 - Prob. 2WE Ch. 7.4 - Prob. 3WE Ch. 7.4 - Prob. 4WE Ch. 7.4 - Prob. 5WE Ch. 7.4 - Prob. 6WE Ch. 7.4 - Prob. 7WE Ch. 7.4 - Prob. 8WE Ch. 7.4 - Prob. 9WE Ch. 7.4 - Prob. 10WE Ch. 7.4 - Prob. 11WE Ch. 7.4 - Prob. 12WE Ch. 7.4 - Prob. 13WE Ch. 7.4 - Prob. 14WE Ch. 7.4 - Prob. 15WE Ch. 7.4 - Prob. 16WE Ch. 7.4 - Prob. 17WE Ch. 7.4 - Prob. 18WE Ch. 7.4 - Prob. 19WE Ch. 7.4 - Prob. 20WE Ch. 7.4 - Prob. 21WE Ch. 7.4 - Prob. 22WE Ch. 7.4 - Prob. 23WE Ch. 7.4 - Prob. 24WE Ch. 7.4 - Prob. 25WE Ch. 7.4 - Prob. 26WE Ch. 7.4 - Prob. 27WE Ch. 7.4 - Prob. 28WE Ch. 7.4 - Prob. 29WE Ch. 7.4 - Prob. 30WE Ch. 7.4 - Prob. 31WE Ch. 7.4 - Prob. 32WE Ch. 7.4 - Prob. 1ST Ch. 7.4 - Prob. 2ST Ch. 7.4 - Prob. 3ST Ch. 7.4 - Prob. 4ST Ch. 7.4 - Prob. 5ST Ch. 7.4 - Prob. 6ST Ch. 7.4 - Prob. 7ST Ch. 7.4 - Prob. 8ST Ch. 7.4 - Prob. 9ST Ch. 7.4 - Prob. 10ST Ch. 7.5 - Prob. 1OE Ch. 7.5 - Prob. 2OE Ch. 7.5 - Prob. 3OE Ch. 7.5 - Prob. 4OE Ch. 7.5 - Prob. 5OE Ch. 7.5 - Prob. 6OE Ch. 7.5 - Prob. 7OE Ch. 7.5 - Prob. 8OE Ch. 7.5 - Prob. 9OE Ch. 7.5 - Prob. 10OE Ch. 7.5 - Prob. 11OE Ch. 7.5 - Prob. 12OE Ch. 7.5 - Prob. 13OE Ch. 7.5 - Prob. 14OE Ch. 7.5 - Prob. 15OE Ch. 7.5 - Prob. 16OE Ch. 7.5 - Prob. 17OE Ch. 7.5 - Prob. 1WE Ch. 7.5 - Prob. 2WE Ch. 7.5 - Prob. 3WE Ch. 7.5 - Prob. 4WE Ch. 7.5 - Prob. 5WE Ch. 7.5 - Prob. 6WE Ch. 7.5 - Prob. 7WE Ch. 7.5 - Prob. 8WE Ch. 7.5 - Prob. 9WE Ch. 7.5 - Prob. 10WE Ch. 7.5 - Prob. 11WE Ch. 7.5 - Prob. 12WE Ch. 7.5 - Prob. 13WE Ch. 7.5 - Prob. 14WE Ch. 7.5 - Prob. 15WE Ch. 7.5 - Prob. 16WE Ch. 7.5 - Prob. 17WE Ch. 7.5 - Prob. 18WE Ch. 7.5 - Prob. 19WE Ch. 7.5 - Prob. 20WE Ch. 7.5 - Prob. 21WE Ch. 7.5 - Prob. 22WE Ch. 7.5 - Prob. 23WE Ch. 7.5 - Prob. 24WE Ch. 7.5 - Prob. 25WE Ch. 7.5 - Prob. 26WE Ch. 7.5 - Prob. 27WE Ch. 7.5 - Prob. 28WE Ch. 7.5 - Prob. 29WE Ch. 7.5 - Prob. 30WE Ch. 7.5 - Prob. 31WE Ch. 7.5 - Prob. 32WE Ch. 7.5 - Prob. 33WE Ch. 7.5 - Prob. 34WE Ch. 7.5 - Prob. 35WE Ch. 7.5 - Prob. 36WE Ch. 7.5 - Prob. 37WE Ch. 7.5 - Prob. 38WE Ch. 7.5 - Prob. 39WE Ch. 7.5 - Prob. 1MRE Ch. 7.5 - Prob. 2MRE Ch. 7.5 - Prob. 3MRE Ch. 7.5 - Prob. 4MRE Ch. 7.5 - Prob. 5MRE Ch. 7.5 - Prob. 6MRE Ch. 7.6 - Prob. 1OE Ch. 7.6 - Prob. 2OE Ch. 7.6 - Prob. 3OE Ch. 7.6 - Prob. 4OE Ch. 7.6 - Prob. 5OE Ch. 7.6 - Prob. 6OE Ch. 7.6 - Prob. 7OE Ch. 7.6 - Prob. 1WE Ch. 7.6 - Prob. 2WE Ch. 7.6 - Prob. 3WE Ch. 7.6 - Prob. 4WE Ch. 7.6 - Prob. 5WE Ch. 7.6 - Prob. 6WE Ch. 7.6 - Prob. 7WE Ch. 7.6 - Prob. 8WE Ch. 7.6 - Prob. 9WE Ch. 7.6 - Prob. 10WE Ch. 7.6 - Prob. 11WE Ch. 7.6 - Prob. 12WE Ch. 7.6 - Prob. 13WE Ch. 7.6 - Prob. 14WE Ch. 7.6 - Prob. 15WE Ch. 7.6 - Prob. 16WE Ch. 7.6 - Prob. 17WE Ch. 7.6 - Prob. 18WE Ch. 7.6 - Prob. 19WE Ch. 7.6 - Prob. 20WE Ch. 7.6 - Prob. 21WE Ch. 7.6 - Prob. 22WE Ch. 7.6 - Prob. 23WE Ch. 7.6 - Prob. 24WE Ch. 7.6 - Prob. 25WE Ch. 7.6 - Prob. 26WE Ch. 7.6 - Prob. 27WE Ch. 7.6 - Prob. 28WE Ch. 7.6 - Prob. 29WE Ch. 7.6 - Prob. 30WE Ch. 7.6 - Prob. 31WE Ch. 7.6 - Prob. 32WE Ch. 7.6 - Prob. 33WE Ch. 7.6 - Prob. 34WE Ch. 7.6 - Prob. 35WE Ch. 7.6 - Prob. 36WE Ch. 7.6 - Prob. 37WE Ch. 7.6 - Prob. 38WE Ch. 7.6 - Prob. 39WE Ch. 7.6 - Prob. 40WE Ch. 7.6 - Prob. 41WE Ch. 7.6 - Prob. 42WE Ch. 7.6 - Prob. 43WE Ch. 7.6 - Prob. 44WE Ch. 7.7 - Prob. 1OE Ch. 7.7 - Prob. 2OE Ch. 7.7 - Prob. 3OE Ch. 7.7 - Prob. 4OE Ch. 7.7 - Prob. 5OE Ch. 7.7 - Prob. 6OE Ch. 7.7 - Prob. 7OE Ch. 7.7 - Prob. 8OE Ch. 7.7 - Prob. 9OE Ch. 7.7 - Prob. 10OE Ch. 7.7 - Prob. 11OE Ch. 7.7 - Prob. 12OE Ch. 7.7 - Prob. 13OE Ch. 7.7 - Prob. 14OE Ch. 7.7 - Prob. 15OE Ch. 7.7 - Prob. 1WE Ch. 7.7 - Prob. 2WE Ch. 7.7 - Prob. 3WE Ch. 7.7 - Prob. 4WE Ch. 7.7 - Prob. 5WE Ch. 7.7 - Prob. 6WE Ch. 7.7 - 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