Standard Form of a Quadratic Function


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.

Vertex Form of Parabola

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:

Vertex of Parabola

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 vertex
h={ - 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=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 Standard Form Calculator again.