Question

Complete the square to put f(x)=2x^2+4x into vertex form.

Answer 1

Answer:

f(x) = 2(x + 1)² - 2

Step-by-step explanation:

The given function is:

`f(x)=2x^2+4x`

Factor 2 out of the expression

`f(x)=2(x^2+2x)`

Use the completing the square rule

`\begin{gathered} f(x)=2(x^2+2x+1^2-1^2) \\ f(x)=2\lbrack(x+1)^2-1\rbrack \end{gathered}`

Expand the expression

`f(x)=2(x+1)^2-2`

Therefore, the vertex form of f(x) = 2x² + 4x is:

f(x) = 2(x + 1)² - 2