Question

In the following exercises, rewrite each function in the $f\left(x\right)=a(x-h{)}^2+k$form by completing the square.

$f\left(x\right)=-3x^2-12x-5$

Short answer

The function upon completing the square is$f\left(x\right)=-3{(x+2)}^2+7$

Step-by-step solution

Given information

Given the equation$f\left(x\right)=-3x^2-12x-5$

Rewrite the equation taking common

Taking common and simplifying, we get

$$\begin{gathered} f\left(x\right)=-3x^2-12x-5 \\ f\left(x\right)=-3(x^2+4x)-5 \\ f\left(x\right)=-3(x^2+2·2·x+2^2)-5+12 \\ f\left(x\right)=-3{(x+2)}^2+7 \end{gathered}$$