Example: y=2x+1
Example (Click to try)
y=2x+1
How to graph your problem
Graph your problem using the following steps:
- Type in your equation like y=2x+1
(If you have a second equation use a semicolon like y=2x+1 ; y=x+3) - Press Calculate it to graph!
Graphing Equations Video Lessons
- Khan Academy Video: Graphing Lines
- Khan Academy Video: Graphing a Quadratic Function
Need more problem types? Try MathPapa Algebra Calculator
Domain and Range Calculator is a free online tool that displays the range and domain for the given function. BYJU’S online domain and range calculator tool makes the calculation faster, and it displays the output in a fraction of seconds.
How to Use the Domain and Range Calculator?
The procedure to use the domain and range calculator is as follows:
Step 1: Enter the function in the input field
Step 2: Now click the
button “Calculate Domain and Range” to get the output
Step 3: Finally, the domain and range will be displayed in the new window
What is Meant by Domain and Range?
In Mathematics, a domain is defined as the set of possible values “x” of a function which will give the output value “y”. It is the set of possible values for the independent variables. The range of a function is defined as the set of resulting values of the dependent variable. These are the set of output
values when the x values are substituted. It is similar that, when the input values are given to the function, it will produce the output.
Also, read: Domain, Codomain and Range of a Function
In short, a domain is defined as the set of values for which the function f(x) is defined, whereas the range is defined as the set of values that the function takes. The domain is called the replacement set, and the range is called the solution set.
Domain of a Function Calculator
Step-by-Step Examples
Algebra
Domain of a Function Calculator
Step 1:
Enter the Function you want to domain into the editor.
The domain calculator allows you to take a simple or complex function and find the domain in both interval and set notation instantly.
Step 2:
Click the blue arrow to submit and see the result!
Created by Bogna Szyk and Wojciech Sas, PhD candidate
Reviewed by Steven Wooding and Jack Bowater
Last updated: Jan 18, 2022
Any time you come across a quadratic formula you want to analyze, you'll find this parabola calculator to be the perfect tool for you. Not only will it provide you with the parabola equation in both the standard form and the vertex form, but also calculate the parabola vertex, focus, and directrix for you.
What is a parabola?
source: Wikimedia
A parabola is a U-shaped symmetrical curve. Its main property is that every point lying on the parabola is equidistant from both a certain point, called the focus of a parabola, and a line, called its directrix. It is also the curve that corresponds to quadratic equations.
The axis of symmetry of a parabola is always perpendicular to the directrix and goes through the focus point. The vertex of a parabola is the point at which the parabola makes its sharpest turn; it lies halfway between the focus and the directrix.
A real-life example of a parabola is the path traced by an object in projectile motion.
The parabola equation in vertex form
The standard form of a quadratic equation is y = ax² + bx + c. You can use this vertex calculator to transform that equation into the vertex form, which allows you to find the important points of the parabola – its vertex and focus.
The parabola equation in its vertex form is y = a(x - h)² + k, where:
- a — Same as the a coefficient in the standard form;
- h — x-coordinate of the parabola vertex; and
- k — y-coordinate of the parabola vertex.
You can calculate the values of h and k from the equations below:
h = - b/(2a)k = c - b²/(4a)Parabola focus and directrix
The parabola vertex form calculator also finds the focus and directrix of the parabola. All you have to do is to use the following equations:
- Focus x-coordinate: x₀ = - b/(2a);
- Focus y-coordinate: y₀ = c - (b² - 1)/(4a); and
- Directrix equation: y = c - (b² + 1)/(4a).
How to use the parabola equation calculator: an example
Enter the coefficients a, b and c of the standard form of your quadratic equation. Let's assume that the equation is y = 2x² + 3x - 4, what means that a = 2, b = 3 and c = -4.
Calculate the coordinates of the vertex, using the formulas listed above:
h = - b/(2a) = -3/4 = -0.75
k = c - b²/(4a) = -4 - 9/8 = -5.125
Find the coordinates of the focus of the parabola. The x-coordinate of the focus is the same as the vertex's (x₀ = -0.75), and the y-coordinate is:
y₀ = c - (b² - 1)/(4a) = -4 - (9-1)/8 = -5
Find the directrix of the parabola. You can either use the parabola calculator to do it for you, or you can use the equation:
y = c - (b² + 1)/(4a) = -4 - (9+1)/8 = -5.25
If you want to learn more coordinate geometry concepts, we recommend checking the average rate of change calculator and the latus rectum calculator.
FAQ
What is a parabola?
A parabola is a symmetrical U shaped curve such that every point on the curve is equidistant from the directrix and the focus.
How do I define a parabola?
A parabola is defined by the equation such that every point on the curve satisfies it. Mathematically, y = ax² + bx + c.
How do I calculate the vertex of a parabola?
To calculate the vertex of a parabola defined by coordinates (x, y):
Find x coordinate using the axis of symmetry formula:
x₀ = - b/(2a)
Find y coordinate using the equation of parabola:
y₀ = c - (b² - 1)/(4a)
How to calculate the focus of a parabola?
To calculate the focus of a parabola defined by coordinates (x, y):
- Find y coordinate using the formula y = c - (b² + 1)/(4a)
- Find x coordinate using the parabola equation.
Bogna Szyk and Wojciech Sas, PhD candidate
What to input?
Standard form: y = ax² + bx + c
Results
Show results using fractions?
Average rate of changeBilinear interpolationCatenary curve… 35 more