Answer:
3x² - 6x + 6 can be written in the form a(x + b)² + c as 3(x - 1)² + 3, where a = 3, b = -1, and c = 3.
Explanation:
To write 3x² - 6x + 6 in the form a(x + b)² + c, we need to complete the square. Here are the steps:
Factor out the coefficient of x² (which is 3 in this case):
3(x² - 2x + 2)
To complete the square, we need to add and subtract (2/2)² = 1 from the expression inside the parentheses:
3(x² - 2x + 1 - 1 + 2)
Rewrite the expression as a perfect square trinomial by grouping the first three terms and factoring:
3((x - 1)² + 1)
Distribute the 3 to simplify:
3(x - 1)² + 3
Therefore, 3x² - 6x + 6 can be written in the form a(x + b)² + c as 3(x - 1)² + 3, where a = 3, b = -1, and c = 3.