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Standard to Vertex Form Calculator
Convert your Quadratic Equation from Standard Form to Vertex Form below.
You will also understand how to
-Convert from Standard Form to Vertex Form – Step by Step.
-Find the Vertex of any Quadratic Equation.
-Find h and k in Vertex Form.
-What are h and k in Vertex Form?
Standard to Vertex Form Calculator
How to use the Standard to Vertex Form Calculator?
Enter the leading coefficients a, b and c in the red box above, next press the red Convert button below to view the Vertex Form of your Quadratic Equation given in Standard Form.
How to convert from Standard 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.
Using the above formula, we get:
h=−b/(2a)=−(8)/(2∗2)=−2
Next, compute k, the vertex y-coordinate, by plugging h = -2 in for x into our quadratic equation:
k=3∗(−2)²+8(−2)+3=−1
Thus, the vertex is
(h,k)=(−2,−1)
Since -(-2)=2 and carrying over the coefficient a=2 we converted to Vertex Form
y=2(x+2)²−1
Watch the video below for a great explanation of how to convert from Standard to Vertex Form.
Example: Convert from Standard Form to Vertex Form
We are given the following Quadratic Equation in 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=3(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.
Video: How to Convert from Standard Form to Vertex Form of a Quadratic Equation
Standard to Vertex Form Calculator
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 created a separate page to learn this method. Complete the Square here .
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)
How do you find the Vertex of a Quadratic Equation?
Every Parabola has either a..
..Minimum (when opened to the top due to leading coefficient a>0) or
..Maximum (when opened to the bottom due to leading coefficient a<0).
The Vertex is just that particular point on the Graph of a Parabola.
See the illustration of the two possible vertex locations below:
Standard to Vertex Form Calculator
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