(a).
To graph: Quadratic function with its vertex, axis of symmetry,
(a).
Answer to Problem 19RE
Function using the vertex and the
Explanation of Solution
Given:
Calculation:
The quadratic function
So,
The graph of a quadratic function
Here, function has a
So the graph opens down.
To find the vertex,
The coordinates of the vertex of a quadratic function of the form
Evaluating
Evaluating
Thus, the vertex is at
The axis of symmetry is the line where
Thus,
To find
Here,
Therefore, the graph has the
Find the discriminant
In case discriminant
Therefore, the graph of the function crosses the
To find out the
The
Factor out
Apply the zero product principle,
Thus, either
Consider
Consider,
Add
Thus, the
Function using the vertex and the
Conclusion:
Quadratic function with its vertex is
(b).
Domain and range of the function.
(b).
Answer to Problem 19RE
Domain is the interval
Explanation of Solution
Given:
Calculation:
Find the domain and range of the function, the domain of
From the graph, find the domain is the interval
Conclusion:
Thus, domain is the interval
(c).
The function is increasing and where it is decreasing.
(c).
Answer to Problem 19RE
The function
Explanation of Solution
Given:
Calculation:
Interval where the function
Also, find where the function is increasing.
From the graph, the function
Conclusion:
Thus, the function
Chapter 3 Solutions
Precalculus
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
University Calculus: Early Transcendentals (3rd Edition)
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