# 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 = ax^{2} + 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 x^{2} 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 = ax^{2} + bx + c

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

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

Where D is discriminant = b^{2} - 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 = 2x^{2} + 3x + 4

**Solution:**

Given: y = 2x^{2 }+ 3x + 4

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

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

D = b^{2} - 4ac

D = -23

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

**Example 2:**

Find the coordinates of the vertex for a given parabola equation y = x^{2} - 5x + 4

**Solution:**

Given: y = x^{2} - 5x + 4

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

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

D = b^{2} - 4ac

D = 9

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

**Example 3:**

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

**Solution:**

Given: y = 4x^{2} + x - 2

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

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

D = b^{2} - 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 = 2x
^{2}+ 4x + 3 - y = 5x
^{2}+ 7x + 5

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