Using the completing-the-square method, rewrite f(x) = x2 − 6x + 2 in vertex form.

Question

f(x) = (x − 3)2
f(x) = (x − 3)2 + 2
f(x) = (x − 3)2 − 7
f(x) = (x − 3)2 + 9

Answer 1

To rewrite the quadratic function \( f(x) = x^2 - 6x + 2 \) in vertex form, we will complete the square.

1. Start with the equation: \[ f(x) = x^2 - 6x + 2 \]

2. Group the \( x \) terms: \[ f(x) = (x^2 - 6x) + 2 \]

3. Complete the square:

   • Take the coefficient of \( x \) (which is -6), divide it by 2 to get -3, and then square it to get 9.
   • We will add and subtract 9 inside the parentheses: \[ f(x) = (x^2 - 6x + 9 - 9) + 2 \]

4. Rewrite the equation: \[ f(x) = ((x - 3)^2 - 9) + 2 \]

5. Combine the constants: \[ f(x) = (x - 3)^2 - 9 + 2 \] \[ f(x) = (x - 3)^2 - 7 \]

Now we have rewritten the function in vertex form. The final result is: \[ f(x) = (x - 3)^2 - 7 \]

Thus, the correct option is: \[ \text{f(x) = (x − 3)² − 7} \]