Question

Find the minimum value of the function f(x) = x2 6x +8

Answer 1

Answer:

- 1

Step-by-step explanation:

Given---> f ( x ) = x² + 6x + 8

To find ---> Minimum value of given function

Solution---> ATQ,

f ( x ) = x² + 6 x + 8

We form whole square here,

f ( x ) = x² + 6 x + 8

We can write 6 as 3 × 2 .

= x² + 2 ( 3 ) ( x ) + 8

= x² + 2 ( 3 ) ( x ) + 8 + 1 - 1

= { x² + 2 ( 3 ) ( x ) + 9 } - 1

= ( x + 3 )² - 1

So for mininimum value of f ( x ) ,

x + 3 = 0

=> x = - 3

Now , minimum value of f ( x ) is

= ( 0 )² - 1

= 0 - 1 = - 1

Answer 2

Step-by-step explanation:

Answer

Given---> f ( x ) = x² + 6x + 8

To find ---> Minimum value of given function

Solution---> ATQ,

f ( x ) = x² + 6 x + 8

We form whole square here,

f ( x ) = x² + 6 x + 8

We can write 6 as 3 × 2 .

= x² + 2 ( 3 ) ( x ) + 8

= x² + 2 ( 3 ) ( x ) + 8 + 1 - 1

= { x² + 2 ( 3 ) ( x ) + 9 } - 1

= ( x + 3 )² - 1

So for mininimum value of f ( x ) ,

x + 3 = 0

=> x = - 3

Now , minimum value of f ( x ) is

= ( 0 )² - = 0 - 1 = - 1