Vertex Form Calculator


How do I find the Vertex Form from the Standard Form?

A Quadratic Equation in Standard Form is
\boxed{ ax^2+bx+c = 0 }

Its Vertex (h,k) can be found from the above Standard Form using
\boxed{ h= {-b \over 2a} , k=f( {-b \over 2a }) }

The Vertex Coordinates (h,k) are plugged into the Vertex Form of a Parabola (see below) as h and k. It is THAT simple.

Vertex Form of Parabola

How do I find the Vertex on the Graph of any Quadratic Equation?

Every Parabola has either a minimum (when opened to the top) or a maximum (when opened to the bottom).
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

Example: Find the Vertex Form of a given Quadratic Equation

We are given the Quadratic Equation
y=3x^2- 6x-2 .
We see that a=3 and b=-6 .
Using a and b, we first compute the x-coordinate of the Vertex as
h={ - b \over 2a}= { -(-6)\over (2*3)} = 1 .
Next, compute the y-coordinate of the Vertex by plugging x=1 into the above equation:
k= 3*(1)^2-6(1)-2=-5 .

Therefore, the Vertex is
(h,k)=(1,-5) .

Thus, we transformed the above Standard Form into the Vertex Form y=(x-1)^2-5 .

Easy, wasn’t it?

Tip: When using the above Vertex Form Calculator to solve
3x^2-6x-2=0 we must enter the 3 coefficients as
a=3, b=-6 and c=-2.

Then, the calculator will find the Vertex (h,k)=(1,-5) step by step.

Finally, the vertex form of the Parabola is y=(x-1)^2-5 .

Get it now? Try the above Vertex Form Calculator again.