Standard Form of a Quadratic Function

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

 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 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.