STANDARD TO VERTEX FORM CALCULATOR

Table of Content (8 min. reading time)

1 – Step by Step Solver: Find the Vertex of any Quadratic Equation
2 – How do you convert from Standard Form to Vertex Form?
3 – How do you locate the Vertex on the Graph of a Parabola?
4 – Example: How do you convert from Standard Form to Vertex Form?
5 – How do I find h and k in Vertex Form?
6 – What are h and k in Vertex Form?

How do you convert from Standard Form to Vertex Form?

The Quadratic Equation in Standard Form is

 y=ax²+bx+c  

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

  h= -b/2a , k=f(h) 

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

Example: Convert from Standard Form to Vertex Form

Let’s convert

y=2x²+8x+3 

into Vertex Form.
Then,
h = -b/(2a) = -(8)/(2*2) = -2 .
Next, compute k, the vertex y-coordinate, by plugging h = -2
into
k = 3*(-2)²+8(-2)+3 = -1 .
Thus, the vertex is (h,k)=(-2,-1) .

Since -(-2)=2 we converted to the Vertex Form

 y=(x+2)²-1 

.

Watch the video below for a great explanation of how to convert from Standard to Vertex Form.

How do you locate the Vertex on the Graph of a 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:

Example: How do you convert from Standard Form to Vertex Form?

We are given the Standard Form

 y=3x²- 6x-2 

.
First, compute the x-coordinate of the vertex
h = – b/2a = -(-6) / (2*3) = 1 .
Next, compute the y-coordinate of the vertex by plugging h=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 to Vertex Form Calculator to solve
3x²-6x-2=0 we must enter the 3 coefficients a,b,c as
a=3, b=-6, c=-2.

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

Finally, the Vertex Form of the above Quadratic Equation is

 y=(x-1)²-5 

Get it now? Try the our Standard Form to Vertex Standard Calculator again.

How do I find h and k in Vertex Form?

There are two ways to find h and k, the vertex x- and y- coordinates. There is a fast way and a long way.

1) The fast way: Given y = ax²+bx+c we first compute h = -b / 2a and next k=f(h) .
Example: y=3x²+6x+4 thus h =-6/2*3 = -1 and
k = f(-1) = 3(-1)²+6(-1)+4 = 3-6+4 = 1
Thus, Vertex Coordinates are (k,h)=(-1,1) .

2) The long way: We do the Complete-the-Square procedure to convert
y=ax²+bx+c into
y=a(x-h)²+k .
We create a separate page to learn this method. Please click HERE to do this procedure.

What are h and k in Vertex Form?

h and k are the Vertex x- and y- coordinates of the Graph of a Quadratic Equation. They give the Location of a Minimum (when a>0) or Maximum (when a<0).

You may also think of h and k as shifts/transformations:
Shifting the Standard Parabola
y=x²
h units right yields
y=(x-h)² .
Shifting it k units up yields
y=(x-h)²+k .
By performing those 2 shifts we moved the Vertex from
the origin (0,0) to the new location (h,k) .