Question

Ewrite the function g(x)=2x²+8x+12 in vertex form by completing the square.

Answer 1

To rewrite the function g(x)=2x²+8x+12 in vertex form, follow the steps of completing the square.

Step-by-step explanation:

To rewrite the function g(x)=2x²+8x+12 in vertex form by completing the square, follow these steps:

1. Identify the coefficient of x², which is 2.
2. Divide the coefficients of x and the constant term by 2 to get 4 and 6, respectively.
3. Complete the square by adding and subtracting the square of half the coefficient of x, which is (4/2)² = 4.
4. Rearrange the terms to obtain the vertex form: g(x) = 2(x+2)²+4.