Question

Express 2x^2-8x+1 in the form of a(x+b)^2+c where a and b are integers.

Answer 1

Answer- 2(x-2)²-3

Explanation:

Greetings !

given expression

`2x {}^(2) - 8x + 1`

Thus, when you change it in the form of

`a(x + b) {}^(2) + c`

we get the expression as

`2(x -2 ) {}^(2) - 3 \\`

simplify it and we get it as

`2(x - 2) {}^(2) - 3 \\ 2(x {}^(2) - 4x + 4) - 3`

Hope it helps!

distribute and multiply

`2x {}^(2) - 8x + 4 - 3 \\ 2x { }^(2) - 8x + 1`

Answer 2

2(x - 2)² - 7

Explanation:

2x² - 8x + 1 ( factor out 2 from the first 2 terms )

= 2(x² - 4x) + 1

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 4x

= 2(x² + 2(- 2)x + 4 - 4) + 1

= 2(x - 2)² - 8 + 1

= 2(x - 2)² - 7