1. Investigating Domain and Range Using Graphs [[173]]

In this lesson, you will explore different representations of quadratic functions, including graphs, verbal descriptions, and tables, and use those representations to determine the domain and range of the quadratic function being represented.
In this section, you will examine graphs of quadratic functions, and learn how to determine the domain and range of a quadratic function from the graph.
A quadratic function is any function that can be written in the form y = ax^{2} + bx + c, where a, b, and c are real numbers, and a ≠ 0. Its graph is a parabola. The constants a, b, and c are called the parameters of the equation. The values of a, b, and c, determine the shape of the parabola.
The domain of a function is the set of xvalues that make that function true. The range of a function is the set of yvalues that make that function true.
Example 1: The quadratic parent function is y = x^{2}. The graph of this function is shown below.
Example 2: The graph of y = –x^{2} + 5 is shown below. Determine the domain and range of this function.
Example 3: The graph of y = 25x^{2} + 2x + 4 is shown below. Determine the domain and range of this function.
Source: Investigating Domain and Range Using Graphs, Texas Education Agency / University of Texas at Austin
2. Investigating Domain and Range Using Verbal Descriptions [[174]]

The DeWind family lives in a rectangular shaped home with a length of 45 feet and a width of 35 feet. Mr. DeWind plans to install carpet in every room of the house with the exception of the square kitchen. The kitchen has a side length of x feet and the function y = 1575 – x^{2} describes the area of the home without the kitchen in square feet. Identify the domain and range of this function.
What is the domain for this situation?
Check Your Answer
Domain: 0 < x < 35, or all real numbers between, but not including, 0 and 35.
What is the range for this situation?
Check Your Answer
Range: 350 < y < 1575, or all real numbers between, but not including, 350 and 1575.
Source: Investigating Domain and Range Using Verbal Descriptions, Texas Education Agency / University of Texas at Austin
3. Join the Course [[259]]

OnTRACK Lessons for Algebra I are supplementary lessons that align with the Texas Essential Knowledge and Skills. The lessons use video, graphics, and online activities to support classroom instruction and facilitate individualized intervention for students. While these lessons are organized as a Project Share “course,” they do not cover every student expectation in the TEKS for the corresponding SBOEapproved course. Students cannot earn course credit by completing OnTRACK lessons.
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