Question

Rewrite the function by completing the square.
f(x) = x² + 12x - 69​

Answer 1

To rewrite the function by completing the square, follow these steps: Take the coefficient of the x-term (12) divided by 2, then square it.

Step-by-step explanation:

To rewrite the function by completing the square, follow these steps:

1. Take the coefficient of the x-term (12) divided by 2, then square it: (12/2)^2 = 36.
2. Add the result from step 1 to both sides of the equation: x^2 + 12x + 36 - 69 = 36 - 69.
3. Simplify: x^2 + 12x + 36 - 69 = -33.
4. Factor the perfect square trinomial: (x + 6)^2 = -33.
5. Take the square root of both sides: x + 6 = ±√(-33).
6. Solve for x: x = -6 ± √(-33).