IntroductionThe domain of a function is all input values that satisfy the function without restriction. Typically the domain is all real numbers; however, in the case of an application problem, one must determine the most reasonable input values that satisfy the given situation. In this lesson, you will practice identifying the domain of a quadratic function given an equation, a graph, and a real-world context.

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5.5.2: Identifying the Domain of a Quadratic Function

Key Concepts• When a quadratic function does not have a specified

interval and is not an application of a real-world situation, its domain is all real numbers.

• This is expressed by showing that the input values exist from negative infinity to infinity as

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5.5.2: Identifying the Domain of a Quadratic Function

Common Errors/Misconceptions• identifying domain with output values rather than with

input values

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5.5.2: Identifying the Domain of a Quadratic Function

Guided Practice

Example 1Describe the domain of the quadratic function g(x) = 1.5x2.

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5.5.2: Identifying the Domain of a Quadratic Function

Guided Practice: Example 1, continued

1. Sketch a graph of the function.

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5.5.2: Identifying the Domain of a Quadratic Function

Guided Practice: Example 1, continued

2. Describe what will happen if the function continues. Looking at the function, you can see that the function will continue to increase upward and the function will continue to grow wider.

Growing wider without end means that the domain of this function is all real numbers as x increases to infinity and decreases to negative infinity, or

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5.5.2: Identifying the Domain of a Quadratic Function

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Guided Practice: Example 1, continued

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5.5.2: Identifying the Domain of a Quadratic Function

Guided Practice

Example 2Describe the domain of the function graphed at right.

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5.5.2: Identifying the Domain of a Quadratic Function

Guided Practice: Example 2, continued

1. Describe what is happening to the width of the function as x approaches positive and negative infinity. The function will continue to open down as x approaches both positive and negative infinity.

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5.5.2: Identifying the Domain of a Quadratic Function

Guided Practice: Example 2, continued

2. Determine the domain of the function. Growing wider without end means that the domain of this function is all real numbers as x increases to infinity and decreases to negative infinity. The domain of the function is all real values,

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5.5.2: Identifying the Domain of a Quadratic Function

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Guided Practice: Example 2, continued

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5.5.2: Identifying the Domain of a Quadratic Function