Put equation 2x^2-4x-4 into y=a(x-h)^2 form

[georgebaseball]

Hello, could you please tell me what I'm doing wrong

the book asks me to write the equation in the form y= a(x-h)^2

this is the equation

2x^2-4x-4

this is how I have been trying to solve it

2 (x^2-2x)-4
2(x^2-2x+1)-4
2(x-1)^2-4
(x-1)^2-2

 

[galactus]

You're OK except for your constant.

There's a formula I use for completing the square that is derived generally and, thus, bypasses the technicalities.

\(\displaystyle \L\\a(x+\frac{b}{2a})^{2}+\underbrace{c-\frac{b^{2}}{4a}}_{\text{constant}}\)

You have a=2, b=-4, c=-4

Enter them in.


But, if you must go through the steps:

\(\displaystyle \L\\2x^{2}-4x=4\)

\(\displaystyle \L\\2(x^{2}-2x)=4\)

\(\displaystyle \L\\2(x^{2}-2x+1)=4+2=6\)

Factor:

\(\displaystyle \L\\2(x^{2}-1)^{2}=6\)

\(\displaystyle \L\\2(x^{2}-1)^{2}-6\)