Question

Rewrite the function f(x) = -3(r +3)? + 11 in the form f(x) = ax? +bx+c.S(x) = 1

Answer 1

Given

`f\mleft(x\mright)=-3\left(x+3\right)^2+11`

Find

Rewrite in the form of

`f\mleft(x\mright)=ax^2+bx+c.`

Step-by-step explanation

Here , we use the identity

`(a+b)^2=a^2+b^2+2ab`

so , the given function becomes

`\begin{gathered} f\mleft(x\mright)=-3\left(x+3\right)^2+11 \\ f(x)=-3(x^2+9+6x)+11 \\ f(x)=-3x^2-27-18x+11 \\ f(x)=-3x^2-18x-16 \end{gathered}`

Final Answer

Therefore , the new function is

`-3x^2-18x-16`