VERTEX TO STANDARD FORM CALCULATOR

y=*(x-)2+


Solution with Steps

Enter Leading Coefficient a and the Vertex (h,k) in the above 3 boxes.
Next, press the button to convert the Vertex to Standard Form of a Parabola with Steps.

How do you convert from Vertex to Standard Form?

The Vertex Form of a Parabola is
y=a(x-h)^2+k
where (h,k) are the Vertex Coordinates.

The Standard form of a Parabola is
y=ax^2+bx+c

To obtain the Standard Form from the Vertex Form we use these steps:
y=a(x-h)^2+k
y=a(x^2-2hx+h^2)+k
y=ax^2-2ahx+ah^2+k

Example: To convert
y=2(x-1)^2-5
we first apply the binomial formula to get
y=2(x^2-2x+1)-5
Next, we distribute the 2 to get
y= 2x^2-4x+2-5
With 2-5=-3 we finally arrive at the Standard Form:
y=2x^2-4x-3


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:

vertex-minimum-maximum

Example: Convert the Vertex Form into the Standard Form?

Standard and Vertex form of a Quadratic Equation
Standard and Vertex form of a Quadratic Equation

We are given the quadratic equation in vertex format
y=2(x+3)^2-7

First, apply the binomial formula
(x+3)^2 = x^2+6x+9

Thus we have
y= 2(x^2+6x+9)-7

Next, distribute the 2 to get
y= 2x^2+12x+18-7

Since 18-7=11 we finally get the standard form
y= 2x^2+12x+11

Here, a=2, b=12 and c=11 are the coefficients in the Standard Form
y= ax^2+bx+c

Get it now? Try the above Vertex to Standard Form Calculator a few more times.