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., $\left(\dfrac{2}{2}\right)^2=1$.

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

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

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

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