Question

Convert f(x) = -3x - 12x - 16 to vertex form by completing the square.

Answer 1

To convert the function f(x) = -3x - 12x - 16 to vertex form, you need to complete the square. The vertex form of the function is f(x) = -3(x + 4)² - 64.

Step-by-step explanation:

To convert the function f(x) = -3x - 12x - 16 to vertex form, we need to complete the square.

Step 1: Group the x-terms together: f(x) = (-3x - 12)x - 16.

Step 2: Factor out a -3 from the first two terms: f(x) = -3(x + 4)x - 16.

Step 3: Complete the square inside the parentheses: f(x) = -3(x + 4)² - 16 - 48.

Step 4: Simplify the constant terms: f(x) = -3(x + 4)² - 64.

The vertex form of the function is f(x) = -3(x + 4)² - 64.