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Vertex to Standard Form Calculator

Vertex to Standard Form Conversion

Convert your Quadratic Equation from Vertex Form to Standard Form below.

You will also understand how to
-Convert from Vertex Form to Standard Form - Step by Step.
-Find the Vertex of any Quadratic Equation.
-Deal with negative Leading Coefficients.

Click below to Start.

Vertex to Standard Form Calculator


How to use the Vertex to Standard Form Calculator?
Enter the leading coefficients a and the vertex (h,k) in the red box above, next press the gray CONVERT button below to view the Standard Form of your Quadratic Equation given in Vertex Form.
How to convert from Vertex to Standard Form?
The Vertex Form of a Parabola is
$$ y=a(x-h)²+k $$ where (h,k) are the Vertex Coordinates.

The Standard form of a Parabola is
$$ y=ax²+bx+c $$

Example: Convert from Vertex to Standard Form

Let $$ y=2(x-1)²-5 $$

we first apply the binomial formula to expand and get
$$ y=2(x²-2x+1)-5 $$

Next, we distribute the 2 to get
$$ y= 2x²-4x+2-5 $$

With 2-5=-3 we finally arrive at the Standard Form:
$$ y=2x²-4x-3 $$



What are the 2 Steps to convert from Vertex to Standard Form?
We obtain the Standard Form from the Vertex Form by using these 2 steps:
Given: $$y=a(x-h)²+k$$
Step1: (Use Binomial Formula) $$y=a(x²-2hx+h²)+k $$
Step2: (Distribute and Combine the like terms ah² and k) $$ y=ax²-(2ah)x+(ah²+k) $$
Vertex to Standard Form Calculator



Video: How to Convert from Vertex Form to Standard Form of a Quadratic Equation

How to Convert from Vertex Form to Standard Form of a Quadratic Equation
How do you find the Vertex of a Quadratic Equation?
Every Parabola has either a..
..Minimum (when opened to the top due to leading coefficient a>0) or
..Maximum (when opened to the bottom due to leading coefficient a<0).
The Vertex is just that particular point on the Graph of a Parabola.
See the illustration of the two possible vertex locations below:

Vertex of Parabola

Vertex to Standard Form Calculator

What if the leading coefficient a is negative?

We are given the quadratic equation in vertex format
$$ y=-2(x+3)²-7 $$
First, apply the binomial formula
$$ (x+3)² = x²+6x+9 $$
Thus we have
$$ y= -2(x²+6x+9)-7 $$

Next, distribute the 2 to get
$$y= -2x²-12x-18-7 $$


Since -18-7=-25 we finally get the standard form
$$ y= -2x²-12x-25$$


Here, $$a=-2, b=-12, c=-25 $$ are the coefficients in the Standard Form
$$ y= ax²+bx+c $$

Get it now? Try our Vertex to Standard Form Calculator a few more times.



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