# What is the vertex form of #y=x^2+3x+2#?

##### 2 Answers

#### Explanation:

The vertex or turning point occurs at the point when the derivative of the function (slope) is zero.

But

Thus the vertex or turning point occurs at

The graph of the function verifies this fact.

graph{x^2+3x+2 [-10.54, 9.46, -2.245, 7.755]}

#### Explanation:

Given:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider just the

We are going to convert this to a 'perfect square' that is not quite equal to it. We then apply a mathematical 'adjustment' such that becomes equal to it.

Change the

Change the

Put it together in the form of

As yet

The adjustment is

So the adjustment is

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute (2) into equation (1) giving: