### 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 isy=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:

### Example: Convert the Vertex Form into the Standard Form?

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.