### Solution with Steps

Enter the 3 coefficients a,b,c of the Quadratic Equation in the above 3 boxes.Next, press the button to find the Vertex and Vertex Form with Steps.

### What you need to know about Standard Form of a Quadratic Function

The Quadratic Equation in Standard Form is

**\**

ax²+bx+c = 0 }

Then, the Vertex(h,k)can be found from the above Standard Form using

\h= {-b \over 2a} , k=f( {-b \over 2a }) }

Once computed, the vertex coordinates are plugged into the Vertex Form of a Parabola, see below.

## Locating the Vertex on the Graph of any Parabola

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:

## Sample Problem: How to convert the Standard Form of a Quadratic Function to Vertex Form

We are given the Standard Form

y=3x²- 6x-2.

First, compute the x-coordinate of the vertexh={ - b \over 2a}= { -(-6)\over (2*3)} = 1.

Next, compute the y-coordinate of the vertex by plugging -1 into the given 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 Standard Form Calculator to solve

3x²-6x-2=0we must enter the 3 coefficients asa=3, b=-6andc=-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 Standard Form Calculator again.