Question

Complete the statements that show y=x^2−2x−1 being converted to vertex form. Form a perfect-square trinomial. y=x^2 −2x−1−_____

A) 1
B) 4
C) 9
D) 16

Answer 1

To convert the equation y=x^2−2x−1 to vertex form, complete the square. The vertex form is y=(x-1)^2-2.

Step-by-step explanation:

To convert the equation y=x^2−2x−1 to vertex form, we need to complete the square. The vertex form of a quadratic equation is y=a(x-h)^2+k, where (h, k) represents the coordinates of the vertex. Let's start:

1. Factor out the coefficient of x^2: y = 1(x^2-2x) - 1
2. Complete the square by taking half of the coefficient of x (-2), square it, and add it inside the parentheses: y = 1(x^2-2x+1) - 1 - 1
3. Simplify: y=1(x-1)^2 - 2

Therefore, the equation y=x^2−2x−1 in vertex form is y=(x-1)^2-2. The answer is option (A) 1.