complete the square

Question

y=x^2-3x-2

 

 

 

 

 

 

 

 

Answer 1

the problem is x^2-3x-2=y, not +2

x^2-3x=2

(-3/2)^2=9/4

x^2-3x+(9/4)=2+(9/4)

x^2-3x+(9/4)=(8/4)+(9/4)

x^2-3x+(9/4)=(17/4)

(x-3/2)^2-(17/4)

Answer 2

y = x² - 3x + 2

 

1) complete square

 

(First, set the equation equal zero).                     x² - 3x + 2 = 0

(Subtract two on both sides of the equal sign).      x² - 3x + 2 - 2 = 0 - 2

                                                                       x² - 3x = -2

(Divide the 2nd coefficient by 2, square it, and add to both sides)

                                                                       x² - 3x + (3/2)² = -2 + (3/2)²

(Evaluate)                                                         x² - 3x + 9/4 = -2 + 9/4

                                                                       x² - 3x + 9/4 = -8/4 + 9/4

(complete the square)                                        (x - 3/2)² = 1/4

(Subtract 1/4 on both sides and re arrange the equation)

                                                                       y = (x - 3/2)² -1/4

Answer 3

Thank you Arthur D.

For x²-3x-2   1/2 the coefficient of x is -3/2

(x-3/2)²=x²-3x+9/4, we want x²-3x-2 so subtract 17/4 and have

x²-3x-2=(x-3/2)²-17/4