Question

which quadratic equation is equivalent to $(x - 4)^2 - (x - 4) - 6 = 0$?
\bigcirc $(u - 4)^2 - (u - 4) - 6 = 0$ where $u = (x - 4)$
\bigcirc $u^2 - (u - 4) - 6 = 0$ where $u = (x - 4)$
\bigcirc $u^2 - 16 - u - 6 = 0$ where $u = (x - 4)$
\bigcirc $u^2 - u - 6 = 0$ where $u = (x - 4)$

Explanation:

Step1: Substitute \( u = (x - 4) \)

We substitute \( u \) for \( (x - 4) \) in the equation \( (x - 4)^2 - (x - 4) - 6 = 0 \).

Step2: Replace \( (x - 4) \) with \( u \)

When we replace \( (x - 4) \) with \( u \), the first term \( (x - 4)^2 \) becomes \( u^2 \), the second term \( -(x - 4) \) becomes \( -u \), and the equation becomes \( u^2 - u - 6 = 0 \) with \( u = (x - 4) \).

Answer:

\( u^2 - u - 6 = 0 \) where \( u = (x - 4) \)