# How to convert from Vertex to Standard Form?

The Vertex Form of a Parabola isy=a(x-h)²+kwhere

**(h,k)**are the Vertex Coordinates.

The Standard form of a Parabola is

y=ax²+bx+c

#### Let’s do an easy example first

Let**y=2(x-1)²-5**

we first apply the binomial formula to expand and get

**y=2(x²-2x+1)-5**

Next, we distribute the 2 to get

**y= 2x²-4x+2-5**

With 2-5=-3 we finally arrive at the Standard Form:

**y=2x²-4x-3**

In general, we obtain the Standard Form from the Vertex Form by using these 2 steps:

Given:

**y=a(x-h)²+k**

Step1: (Use Binomial Formula)

**y=a(x²-2hx+h²)+k**

Step2: (Distribute and Combine 2 like terms ah² and k)

**y=ax²-(2ah)x+(ah²+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:

### Example: What if the leading coefficient a is negative?

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

First, apply the binomial formula ** (x+3)² = x²+6x+9 **

Thus we have **y= -2(x²+6x+9)-7 **

Next, distribute the 2 to get **y= -2x²-12x-18-7 **

Since -18-7=-25 we finally get the standard form

**y= -2x²-12x-25**

Here, **a=-2, b=-12** and **c=-25** are the coefficients in the Standard Form **y= ax²+bx+c **

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