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# Vertex Form Calculator

Choose the equation form and enter the values of **a**,** b**, and **c** in the vertex form calculator to find vertex and y-intercept.

Table of Contents:

## Vertex Form Calculator

The vertex form calculator is used to find the vertex and y-intercept for a parabola. You can find the vertex for a standard quadratic form and vertex form of a parabola.

## What is a vertex?

A vertex is the intersection point of the x and y coordinates of a parabola. It is the extremal point on its graph. It can be a minimum or maximum point.

The point is generally written as p(h,k). Here **h** is the x-coordinate and **k** is the y-coordinate.

## Vertex formula:

Vertex is calculated from two types of equations: standard and vertex form.

### For standard form (y = ax^{2} + bx + c):

h = -b/2a

k = c - b^{2}/(4a)

(Alternatively, you can convert standard form into vertex form to identify the values.)

### For vertex form (y = a*(x-h)^{2} + k) :

Simply identify **h** and **k**.

## How to calculate the vertex of a parabola?

**Example: **

Find the vertex for the equation:

y = 3x^{2 }+ 2x + 5

**Solution:**

**Step 1:** Complete the square:

y = x^{2} + 2x + 5

y - 5 + 1 = x^{2} + 2x +1 (Adding 1 to the both sides)

y - 4 = (x + 1)^{2}

y = (x + 1)^{2} + 4

Now it is in vertex form.

**Step 2:** Identify h and k: