How To Find Domain Of A Parabola
Determining the Domain and Range for Quadratic Functions
Resource ID: A1M6L1
Grade Range: 9 - 12
Allow'southward Get Started
Given a state of affairs that tin can exist modeled by a quadratic function or the graph of a quadratic function, make up one's mind the domain and range of the part.
TEKS Standards and Student Expectations
A(vi) Quadratic functions and equations. The educatee applies the mathematical process standards when using properties of quadratic functions to write and stand for in multiple means, with and without engineering, quadratic equations. The student is expected to:
A(6)(A) make up one's mind the domain and range of quadratic functions and represent the domain and range using inequalities
Resource Objective(s)
To determine the domain and range of a quadratic office when given a argument or graph.
Essential Questions
How do you determine the domain and range of a quadratic role when given its graph?
How do yous decide the domain and range of a quadratic role when given a verbal statement?
Vocabulary
- Quadratic Equation
- Parabola
- Domain
- Range
Investigating Domain and Range Using Graphs
We're going to explore dissimilar representations of quadratic functions, including graphs, exact descriptions, and tables. We'll determine the domain and range of the quadratic function with these representations.
Let's beginning examine graphs of quadratic functions, and larn how to determine the domain and range of a quadratic role from the graph.
A quadratic equation is any equation/part with a caste of two that tin exist written in the form y = aten 2 + bten + c, where a, b, and c are existent numbers, and a does not equal 0. Its graph is called a parabola. The constants a, b, and c are called the parameters of the equation. The values of a, b, and c make up one's mind the shape and position of the parabola.
The domain of a function is the fix of all real values of x that will give real values for y. The range of a function is the prepare of all real values of y that yous can get by plugging existent numbers into 10.
Case 1
The quadratic parent function is y = x 2. The graph of this function is shown beneath.
Example 2
The graph ofy = -x 2 + 5 is shown beneath. Decide the domain and range of the role, and check to meet if y'all interpreted the graph correctly.
Example 3
The graph ofy = 2510 2+ 4 is shown beneath. Make up one's mind the domain and range of this function. Drag the appropriate values into the boxes below the graph.
Practise Activity—Quadratic Part Explorer
1. Using the interactive link in a higher place, move the sliders to adjust the values of the coefficients: a, b, and c. Find how the graph changes when you movement these sliders.
ii. Continue to adjust the values of the coefficients until the graph satisfies the domain and range values listed beneath. Tape the role and its corresponding domain and range in your notes.
Domain: –∞ < x < ∞, Range: y ≥ 0
Domain: –∞ < x < ∞, Range: y ≤ -v
Domain: –∞ < x < ∞, Range: y ≥ 2
Investigating Domain and Range Using Verbal Descriptions
Sometimes you will be presented a trouble in verbal form, rather than in symbolic form. In order to determine the domain and range of a quadratic role from the verbal statement information technology is oft easier to use the verbal representation—or give-and-take problem—to generate a graph. Past using this word problem, yous tin can more conveniently observe the domain and range from the graph.
Click on the image to access the video and follow the instructions:
- Watch the video. When asked to place the true statement regarding the independent and dependent variable, choose A, B, or C.
- Record the case problem and the table of values for t and h.
- After the graph is drawn, identify the domain and range for the function, and record it in your notes. Judge the maximum value of t for the domain.
Use your graphing calculator or an online graphing calculator for the post-obit examples. Graph the functions to determine the domain and range of the quadratic function.
Example 4
A bird is building a nest in a tree 36 feet above the ground. The bird drops a stick from the nest. The role f(ten) = -16x two + 36 describes the height of the stick in feet after x seconds. The graph of this function is shown below. Identify the domain and range of this function using the drag and drop activity below.
Example 5
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 carpeting in every room of the business firm, with the exception of the square kitchen. The kitchen has a side length ofx feet. The functiony = 1575 - x 2 describes the area of the dwelling in foursquare feet, without the kitchen. Identify the domain and range of this office.
Vocabulary Activity
Journal Activity
Source: https://www.texasgateway.org/resource/determining-domain-and-range-quadratic-functions-0#:~:text=The%20values%20of%20a%2C%20b,plugging%20real%20numbers%20into%20x.&text=The%20quadratic%20parent%20function%20is%20y%20%3D%20x2.
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