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Vertex Form Calculator

$$ f(x) = A (x - H)^2 + K $$

Table of Content


A vertex form calculator is an online tool designed to make it super easy for you to figure out the vertex form (highest or lowest point) of a quadratic equation, which is essential in graphing and understanding the shape of a parabola curve.

What is a Vertex Form of Parabola? 

In Mathematics,

“The vertex form is one of the main ways of representing the equation of a parabola, which is a U-shaped curve”.

Before we dive into the Vertex Form Calculator usage, let's quickly understand the concept of a parabola. A parabola is like the shape of a water fountain when it shoots water into the air and then gravity pulls it back down.

It's a curve that describes the concept of a parabola. You can also use a parabola vertex calculator to get this curve for a given second-degree equation.

Vertex Form Expressions:

The formula of vertex form is as follows:

y = a(x - h)² + k


  • y  =  Y-coordinate
  • a  =  Coefficient
  • x  =  X-coordinate
  • h  =  Vertex of the parabola
  • k  =  Vertex of the parabola

In this formula,

  • y represents the vertical position on the graph.
  • a is the coefficient that identifies the steepness or width of the parabola. If ‘a’ is positive, the parabola opens upward, and if 'a' is negative, then it opens downward.
  • x represents the horizontal position on the graph.
  • h is a constant value that tells you where the parabola is horizontally positioned. If ‘h’ is positive, the parabola shifts to the right, and if it's negative, it shifts to the left.
  • k is the vertical shift that tells you where the parabola is vertically positioned. If ‘k’ is positive, the parabola shifts upward, and if it's negative, it shifts downward.

How to Find Vertex Form?

Let's solve a simple vertex form example step by step:

Vertex Form Equation: y = a(x - h)² + k

Suppose we have the equation: y = 3(x - 2)² + 1

'a' represents the shape of the curve. In this case, it's positive, so the curve opens upward.

'(h, k)' represents the vertex of the parabola. Here, (2, 1) is our vertex. The 'h' value (2) shifts the parabola horizontally, and the 'k' value (1) shifts it vertically. So, our vertex is at (2, 1).

Now, if we want to find 'y' when 'x' is 3, we plug it into the equation:

y = 3(3 - 2)² + 1

First, we calculate inside the brackets:

y = 3(1)² + 1

Then, we square 1:

y = 3(1) + 1

Now, we multiply 3 by 1:

y = 3 + 1

Finally, we add 3 and 1:

y = 4

So, when 'x' is 3, 'y' is 4. This gives us a point on the parabola. You can repeat this process for different 'x' values to plot more points and sketch the parabolic curve. You can also find these values from the vertex calculator.

Steps to Use Vertex Form Calculator:

Using this free online tool vertex form calculator you can easily find the vertex form by entering some inputs such as:

What to do:

  • Select which form type you want to calculate
  • Enter the variables according to the equation
  • Press the Calculate button

What you get:

  • The vertex and standard form of the given equation.
  • The standard form to vertex form calculator displays the characteristic points with a parabola graph.


What’s the difference between vertex form and standard form?

Here's a list that describes the main differences between vertex form and standard form for quadratic equations:

Vertex Form:

Written as y = a(x - h)² + k.

  • Easily reveals the vertex of the parabola at the point (h, k).
  • The 'a' value determines the direction and steepness of the parabola.
  • Convenient for graphing and understanding the vertex and transformations.
  • Commonly used when focusing on the vertex and shape of the parabola.

Standard Form:

  • Written as ax² + bx + c = 0, where a, b, and c are constants.
  • Doesn't directly provide information about the vertex; additional calculations are required.
  • Coefficients 'a' and 'b' influence the position and shape of the parabola.
  • Typically used for solving quadratic equations and finding x-intercepts.
  • More suitable for working with equations and solving for 'x'.

References: How to Find the Vertex, Using the Vertex Formula, and Completing the Square


Alan Walker

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.

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