Question

Complete the square to transform the expression x2 − 2x − 2 into the form a(x − h)2 + k. (x − 1)2 + 3 (x − 1)2 − 3 (x − 2)2 − 3 (x − 2)2 + 3

Answer 1

To complete the square and transform the expression x^2 - 2x - 2 into the form a(x - h)^2 + k, we can follow these steps:

Step 1: Take the coefficient of x, which is -2, divide it by 2, and square the result:

-2 ÷ 2 = -1

(-1)^2 = 1

Step 2: Add the result from Step 1 to both sides of the equation:

x^2 - 2x - 2 + 1 = x^2 - 2x - 1

Step 3: Rewrite the expression on the left side as a perfect square trinomial:

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

Step 4: Simplify the expression on the right side:

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

Therefore, the expression x^2 - 2x - 2 can be written in the form a(x - h)^2 + k as (x - 1)^2 - 1.