Question

Write 1+x-2x^2 in the form if p-2(x-q)^2

Answer 1

9/8 - 2 ( x - ¼ )²

Explanation:

Rearrange 1 + x - 2x²,

-2x² + x + 1

Factor -2 ,

= -2 ( x² - ½x ) + 1

Using Completing the Square Method,

= -2 [ x² - ½x + (-¼)² - (-¼)² ] + 1

= -2 [ ( x - ¼ )² - (-¼)² ] + 1

= -2 ( x - ¼ )² - (-2) (-¼)² + 1

= -2 ( x - ¼ )² + 2 (-¼)² + 1

= -2 ( x - ¼ )² + ⅛ + 1

= -2 ( x - ¼ )² + 9/8

= 9/8 - 2 ( x - ¼ )²