Point of order--"domain", "range", and "inverse" are things associated with functions, whereas a "parabola" is a shape. You need to find the domain, range, and inverse of a quadratic function, the graph of which is a parabola. Step one, then, could be to find the quadratic equation in question explicitly. Are you familiar with the "vertex form" of a quadratic equation? That would be the easiest way to start, since the coordinates of the vertex appear in the equation, and you know what those are. After that, here are the questions that you want to ask yourself: Are there any values of x that cannot be plugged into this equation? If there are, those are numbers which are not in the domain. Everything else will be (and that could mean that the domain is "everything"). What values of y can I get out of this equation? Try some different values of x and see what you get if the answer to this doesn't jump out at you. All the different possible y's that you can get are in the range. (Once you have answered those questions, take a look at the parabola itself. There are geometric reasons for those answers as well. There is a way to just look at the graph and know what the domain and range are. But it's easier to see that with the answer in hand.) The inverse is a harder question to figure out. This quadratic equation won't be invertible. Every value of y will have two "preimages". If you restrict the domain artificially you could get an inverse. Answer from InfanticideAquifer on reddit.com
Study.com
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How to Find the Domain and Range From the Graph of a Parabola | Algebra | Study.com
Domain: The domain of a graph is the set of {eq}x {/eq} values which result in a valid output, {eq}y {/eq}. Range: The range of a graph is the set of valid outputs, {eq}y {/eq}, yielded by inputs {eq}x {/eq}. Parabola: A parabola is roughly ...
Cuemath
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Parabolic function | Domain and range of a quadratic function
It is advisable to look at graphs for such observations: ... Upon putting any values of x into the quadratic function, it remains valid and existing throughout. So, I can say that its domain is all x values. But the range of a parabola is a little trickier.
Videos
04:41
Finding Domain & Range - with Parabolas
Domain and Range #grade10 #math #mathgrade10 | TikTok
How To Find The Domain and Range of a Quadratic Function - YouTube
07:39
Determine the vertex and domain and range of a function - YouTube
04:16
Domain and Range of Quadratic Functions Tutorial - YouTube
02:01
Graphing Parabolas - Domain and Range
CK-12 Foundation
ck12.org › all subjects › algebra i › domain and range › how to find the domain and range of a parabola?
Flexi answers - How to find the domain and range of a parabola? | CK-12 Foundation
September 11, 2025 - The domain and range of a parabola depend on its orientation and the vertex of the parabola. The domain of every quadratic equation trinomial of the form @$\begin{align*}ax^2+bx+c=0\end{align*}@$ is all real numbers @$\begin{align*}(\mathbb{R})\end{align*}@$. The range of a parabola depends ...
Reddit
reddit.com › r/learnmath › how to get the domain ,range and inverse of a parabola that opens upward with the vertex of (4,0)?
r/learnmath on Reddit: How to get the domain ,range and inverse of a parabola that opens upward with the vertex of (4,0)?
October 10, 2021 -
Please help me I don't really know know to get the domain and range with this much limited info.
Top answer 1 of 3
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Point of order--"domain", "range", and "inverse" are things associated with functions, whereas a "parabola" is a shape. You need to find the domain, range, and inverse of a quadratic function, the graph of which is a parabola. Step one, then, could be to find the quadratic equation in question explicitly. Are you familiar with the "vertex form" of a quadratic equation? That would be the easiest way to start, since the coordinates of the vertex appear in the equation, and you know what those are. After that, here are the questions that you want to ask yourself: Are there any values of x that cannot be plugged into this equation? If there are, those are numbers which are not in the domain. Everything else will be (and that could mean that the domain is "everything"). What values of y can I get out of this equation? Try some different values of x and see what you get if the answer to this doesn't jump out at you. All the different possible y's that you can get are in the range. (Once you have answered those questions, take a look at the parabola itself. There are geometric reasons for those answers as well. There is a way to just look at the graph and know what the domain and range are. But it's easier to see that with the answer in hand.) The inverse is a harder question to figure out. This quadratic equation won't be invertible. Every value of y will have two "preimages". If you restrict the domain artificially you could get an inverse.
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Unique inverse cannot be determined for any bijective interval with the given information
Sciencing
sciencing.com › range-parabolas-10027670
How To Find The Range Of Parabolas - Sciencing
March 24, 2022 - A parabola has a domain and range that are dependent upon the vertex, or its central point, and the direction in which the "U" shape opens. The range is the set of all numbers that can hold a value for ...
Texas Gateway
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Determining the Domain and Range for Quadratic Functions | Texas Gateway
The domain of a function is the set of all real values of x that will give real values for y. The range of a function is the set of all real values of y that you can get by plugging real numbers into x. ... The quadratic parent function is y = x2. The graph of this function is shown below.
Cuemath
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How to find the domain and range of a parabola? [Solved]
Step 2: In any graph, we can have the domain as all the x – coordinate values (along the x-axis) of the graph. Step 3: The range is all y – coordinate values (along the y-axis) of the graph.
Math Monks
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Domain and Range of a Parabola With Examples & Diagrams
November 19, 2024 - Thus, the domain is x ∈ (-∞, ∞) Since the coefficient of x2 is 1 (positive), the parabola opens upwards. To find the range, we first complete the square to express the quadratic in the vertex form.
YouTube
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Domain and Range of a Parabola (Grade 10,11 and 12 Mathematics) - YouTube
How to find the domain and range of a parabola (quadratic function)For Grade 10, 11 and 12 Mathematics (NSC, CAPS)Download Math Study Notes at https://payhip...
Published June 15, 2022
Quora
quora.com › How-do-you-find-the-domain-and-range-of-a-parabola-which-is-not-infinite
How to find the domain and range of a parabola which is not infinite - Quora
Answer (1 of 3): A parabola is a two-dimensional curve that can be either open or closed. It is defined by a quadratic equation, which means that its highest or lowest point (known as the vertex) will always lie on the line y = x^2. A parabola can be either infinite or finite, depending on its sh...
Mometrix
mometrix.com › home › domain and range of quadratic functions
Domain and Range of a Quadratic Function (Video & Practice Questions)
June 29, 2013 - And the range for this graph is all real numbers greater than or equal to -3. As you can see, the turning point, or vertex, is part of what determines the range. The other is the direction the parabola opens. If a quadratic function opens up, then the range is all real numbers greater than or equal to the \(y\)-coordinate of the range.
YouTube
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Finding Domain & Range - with Parabolas - YouTube
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Published February 20, 2013 Views 169K
Mashup Math
mashupmath.com › blog › how-to-find-domain-and-range-of-a-graph
How to Find Domain and Range of a Graph (Step-by-Step) — Mashup Math
April 9, 2024 - Remember that the domain refers to all of the possible x-values, and the range refers to all of the possible y-values. Let’s start with finding the domain of this graph. Notice that the graph is a parabola that extends forever on both the ...
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CK-12 Foundation
ck12.org › all subjects › algebra i › domain and range › how do you find the domain and range of a parabola?
Flexi answers - How do you find the domain and range of a parabola? | CK-12 Foundation
April 2, 2025 - The domain and range of a parabola depend on its orientation and the vertex of the parabola. The domain of every quadratic equation trinomial of the form @$\begin{align*}ax^2+bx+c=0\end{align*}@$ is all real numbers @$\begin{align*}(\mathbb{R})\end{align*}@$. The range of a parabola depends ...
Effortless Math
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How to Find the Domain and Range of Quadratic Functions - Effortless Math: We Help Students Learn to LOVE Mathematics
Here is a step-by-step guide to finding the domain and range of quadratic functions: Delve into the quintessence of quadratic functions, characterized by a parabolic graph that either opens upwards or downwards. They bear the general form \(y=ax^2+bx+c\), where, \(a,b\), and \(c\) are real numbers and \(a≠0\). Consider also the vertex, a pivotal point that serves as the function’s pinnacle or nadir. The axis of symmetry, a vertical line that bisects the parabola, is instrumental in understanding its geometric idiosyncrasies.
Teachers Pay Teachers
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Domain and range parabolas | TPT
Range given a Table, Mapping, Equation, points on a graph, ordered pairs, 3. Finding ... **This resource is 100% editable.** Teach your Algebra students how to find the properties (characteristis) of a · parabola including the vertex, axis of symmetry y-intercept, zeros,
IL Classroom
ilclassroom.com › lesson_plans › 8962-determine-the-domain-and-range-of-a-parabola-looking-at-the-graph
Determine the domain and range of a parabola: looking at the graph | IL Classroom
In this lesson you will learn how to determine the domain and range of a parabola by looking at the graph.
Mathspace
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Domain and range of quadratic functions | Grade 12 Math | Ontario 12 Mathematics for College Technology (MCT4C) | Mathspace
If the function has been defined over its natural domain, there is always either a maximum or a minimum function value. At the opposite extreme, the range extends to either $-\infty$−∞ or $\infty$∞, meaning there is no bounding value apart from the maximum or minimum. When looking at parabolas, we will most often find that the domain is all real $x$x, also written as the set $\left(-\infty,\infty\right)$(−∞,∞), and that the range is either $\left[\text{min value},\infty\right)$[min value,∞) for concave up parabolas, or $\left(-\infty,\text{max value}\right]$(−∞,max value] for concave down parabolas.