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

Question

asked May 23, 2022 11.9k views

1 Answer

Ludovic · Answer 1 · 2022-05-28T03:22:53+0000

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
.