Complete the square to determine the minimum or maximum value of the function defined by the expression. x2 + 4x + 3

Complete the square = ( x + 2 )² - 1

minimum = (-2 , 1 )

Step-by-step explanation:

Given the equation = x² + 4x + 3

To find,

Minimum by completing square

Completing Square:

x² + 4x

( x + 2 )²- 2²      Divide 4 by 2 , Add and subtract the answer

( x + 2 )² - 4

x² + 4x + 3

( x + 2 )² - 4  + 3

( x + 2 )² - 1

The minimum of the graph form is y = a(x + b)² - c at co ordinates (-b , c)

So, the minimum is at (-2 , 1 )

..

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x