Algebra

STANDARD TO VERTEX FORM CALCULATOR

Published by
Mike Woodhill PhD








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.
Learn how to find the Vertex Form using this helpful Video on YouTube. She is truly the expert!


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) .

Mike Woodhill PhD

As a long time instructor I would like you to benefit from my Step by Step Calculators. You may also schedule a live tutoring session to succeed in your class. 😉

Published by
Mike Woodhill PhD

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