Given
[tex]f\mleft(x\mright)=-3\left(x+3\right)^2+11[/tex]
Find
Rewrite in the form of
[tex]f\mleft(x\mright)=ax^2+bx+c.[/tex]
Explanation
Here , we use the identity
[tex](a+b)^2=a^2+b^2+2ab[/tex]
so , the given function becomes
[tex]\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}[/tex]
Final Answer
Therefore , the new function is
[tex]-3x^2-18x-16[/tex]
