Vertex Calculator

The vertex of a parabola is defined as the point where exactly it turns. It is also called the minimum point. The vertex formula helps to find the vertex coordinates of a parabola. The standard form of a parabola is y = ax² + bx + c. The vertex form of the parabola y = a(x - h)² + k.The vertex at which the parabola is minimum (when the parabola opens up) or maximum (when the parabola opens down) and the parabola turns (or) changes its direction.

What is Vertex Calculator?

'Vertex Calculator' is an online tool that helps to calculate the coordinates of the vertex point for a given parabola equation. Online Vertex Calculator helps you to calculate the coordinates of the vertex point within a few seconds. If the coefficient x² is positive then the vertex is the bottom of the U- shaped curve and if it is negative the vertex point is the top of the U-shaped curve.

Vertex Calculator

How to Use Vertex Calculator?

Please follow the steps below on how to use the calculator:

• Step1: Enter the coefficients of a, b, and c in the given input boxes.
• Step 2: Click on the "Solve" button to find the coordinates of the vertex point.
• Step 3: Click on the "Reset" button to clear the fields and enter new values.

How to Find Vertex?

In the standard form, we write the quadratic equation as y = ax² + bx + c

In the standard form, the vertex (V) of the parabola is given by

V = (-b/2a, -D/4a)

Where D is discriminant = b² - 4ac

The vertex equation of a parabola is of the form y = a(x - h)² + k

The vertex of the parabola is at the coordinate (h, k)

The vertex of the parabola (h, k) = (-b/2a, -D/4a)

Let's see an example to understand briefly.

Solved Examples on Vertex Calculator

Example 1:

Find the coordinates of the vertex for a given parabola equation y = 2x² + 3x + 4

Solution:

Given: y = 2x² + 3x + 4

Here a = 2, b = 3, c = 4

The vertex of the parabola (h, k) = (-b/2a , -D/4a)

D = b² - 4ac

D = -23

(h, k) = (-3/4, -23/8)

Example 2:

Find the coordinates of the vertex for a given parabola equation y = x² - 5x + 4

Solution:

Given: y = x² - 5x + 4

Here a = 1, b = -5, c = 4

The vertex of the parabola (h, k) = (-b/2a, -D/4a)

D = b² - 4ac

D = 9

(h , k) = (5/2, -9/4)

Example 3:

Find the coordinates of the vertex for a given parabola equation y = 4x² + x - 2

Solution:

Given: y = 4x² + x - 2

Here a = 4, b = 1, c = -2

The vertex of the parabola (h, k) = (-b/2a, -D/4a)

D = b² - 4ac

D = 33

(h , k) = ( -1/8, -33/16)

Similarly, you can try the calculator to find the coordinates of the vertex for a given parabola equation

• y = 2x² + 4x + 3
• y = 5x² + 7x + 5

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• Vertex
• Polar Coordinates

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