Why you need to convert the Standard form into the vertex form



Updated: June 16, 2024

The parabola equation can be shown in multiple ways such as standard, vertex or intercept form. You can easily convert one form to the other as per your requirement. Vertex form is another way to write the parabola equation.

Standard Form:

The standard from of a parabola is:

y=ax2+ bx+ c.

Now here a and b are real numbers where a 0 and x, y are variables that show a point on the parabola. A is the constant that tells us that the parabola will open upward or downward. Here h and k present the locations of the vertex.

Vertex Form:

The vertex form is:

y=a(x-h)2 +k.

In this form a, hand k are real numbers where a 0 and x, y presents a point on the parabola.

What is the Vertex?

The meeting point of two lines and curves is called the vertex. When two lines meet at a point then they form an angle and this is the inner angle.

Why do we convert to Vertex form?

It is an alternative way to write out your equation of parabola. Vertex form is useful for solving quadratic equations, for creating graphs and much more. From the vertex form it is easy to calculate the roots of the equation that shows where the parabola hits the x-axis.

However, the standard form is less helpful as compared to the vertex form when finding out the vertex of the parabola. Finding vertex manually will take a lot of your time and efforts but if you want to save your time then visit calculator-online.net website. It offers a free and precise Vertex form calculator that you can utilize to convert the standard form to vertex and vice versa effortlessly.

How to Convert Standard Form to Vertex Form?

Use the Completing square technique to convert standard form to vertex form.

Go through the below listed steps:

  • The standard form: m= ax2 + bx +c.
  • Now the first thing you have to do is to have a common from the first two terms: m = a(x2+bxa)+c.
  • Complete the square for expression x. After that add and subtract (b/2a)2 from the equation: m = a[(x2+bxa)+(b2a)2-(b2a)2]+c.
  • Now we can write it as: m = a[(x+(b2a))2-(b2a)2]+c.
  • m = a[(x+(b2a))2-b4a2]+c.

Now compare it with the vertex equation: m = a(x – h)2 + k, the vertex h = -b2a and k = c -b24a.Instead of going through this long process, you can easily get the assistance of a free vertex form calculator to transform the standard form to vertex form precisely.

How to find the vertex?

Example: Lets convert y= 2×2 + 8x +3.

Given that:

h= -b2a.

h = -84= -2.

Now put the value of the x coordinate in the equation to find out the value of the y coordinate:

y= 2(-2)2 + 8(-2) +3.

y= 2(4) + (-16) +3.

y= 8 -16 +3.

y= -5 .

So the vertex of the equation is (-2, -5). Now by plugging the values into vertex form:

y=a(x-h)2 +k.

Now the vertex form equation is:

y=2(x+2)2 -5.

For this, you can also find the vertex calculator that lets you convert standard form to vertex form or helps to calculate the vertex conveniently.

How to Convert a Standard Form to a Vertex Form Online?

Read the below listed steps to convert standard from to vertex form online:

Step 1: Firstly, choose the “convert standard to vertex form” option from the drop down menu of the vertex form calculator.

Step 2: Add the values of the A, B and C in the specified places and hit the calculate button.

Step 3: Press the download icon to export the results in PDF format from the vertex formula calculator.


Many ways are available to convert standard form to vertex form but the fastest and reliable way is an online vertex form calculator that lets you perform countless conversions without charging any cost.