Question

Rewrite the function by completing the square.
(f(xW
d. -6

Answer 1

To rewrite a function by completing the square, follow these steps: group the x terms, complete the square, factor the perfect square trinomial, and write the function in vertex form.

Step-by-step explanation:

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

1. Group the x terms and constant terms separately.
2. Complete the square by adding the square of half the coefficient of the x term.
3. Factor the perfect square trinomial and simplify.
4. Write the function in vertex form.

For example, if the function is f(x) = x² + 4x - 6, we can complete the square as follows:

1. Group the x terms: f(x) = (x² + 4x) - 6.
2. Complete the square: f(x) = (x² + 4x + (4/2)²) - (4/2)² - 6.
3. Factor the perfect square trinomial: f(x) = (x + 2)² - 10.
4. Write the function in vertex form: f(x) = (x + 2)² - 10.