Question

Express y= x² + 2x + 3 in the form of y= (x-h)² + k​

Answer 1

Given:

The equation is

`y=x^2+2x+3`

To find:

The vertex form of the given equation, i.e.,
`y=x^2+2x+3`.

Solution:

We have,

`y=x^2+2x+3`

It can be written as

`y=(x^2+2x)+3`

Add and subtract square of half of coefficient of x, i.e.,
`\left((2)/(2)\right)^2=1`.

`y=(x^2+2x+1)-1+3`

`y=(x^2+2(x)(1)+1^2)+2`

`y=(x+1)^2+2`
`[\because (a+b)^2=a^2+2ab+b^2]`

Therefore, the required form of given function is
`y=(x+1)^2+2`.