Question

At which value of x the function y=x^(2)+6x+12 is minimum?

Answer 1

Answer:

- 3

Step-by-step explanation:

⇒ x^2 + 6x + 12

⇒ x^2 + 6x + 9 + 3

⇒ x^2 + 6x + ( 3 )^2 + 3

⇒ x^2 + 2( 3 * x ) + ( 3 )^2 + 3

⇒ ( x + 3 )^2 + 3

 Square of any number can't be lesser than 0, so the minimum value of ( x +  3 )^2 can be 0.

This means :

    ⇒ ( x + 3 )^2 = 0

    ⇒ x + 3 = 0

    ⇒ x = - 3

Hence for x = - 3, value of the given function is minimum.

Answer 2

Step-by-step explanation:

Aloha !

$\text { This is Sweety Adihya }$

y=x²+6x+12

=x²+6x+9+3

=x²+6x+3²+3

=x²+2(3× X) +3²+3

=(x+3)²+3

Taking,

(x+3)²=0

(x+3)=0

x= -3

Hope it will help you

@ Sweety Adihya