Question

express the quadratic function f(x)=3x^2 + 6x - 2 in the form a(x + h)^2 + k where a,h and k are constants

Answer 1

Step-by-step explanation:

Given:

`f(x)=3x^2+6x-2`

First, we do completing the square on the given function to express it into vertex form. So,

We write it in the form:

`\begin{gathered} x^2+2ax+a^2 \\ \end{gathered}`

And, factor out 3: So,

`\begin{gathered} 3(x^2+2x-(2)/(3)) \\ \text{where:} \\ 2a=2\text{ or a=1} \\ \text{Hence} \\ 3(x^2-2x-(2)/(3)+1^2-1^2) \end{gathered}`

Since:

`\begin{gathered} x^2+2ax+a^2=(x+a)^2 \\ So, \\ x^2+2x+1^2=(x+1)^2 \end{gathered}`

Then,

`\begin{gathered} 3(x^2-2x-(2)/(3)+1^2-1^2) \\ =3((x+1)^2-(2)/(3)-1^2) \\ \text{Simplify} \\ f(x)=3(x+1)^2-2-3 \\ f(x)=3(x+1)^2-5 \end{gathered}`

Therefore, the answer is:

`f(x)=3(x+1)^2-5`