Rewrite the function $f(x)=2(x+2)^{2}-5$ in the form $f(x)=a x^{2}+b x+c$.
\[
f(x)=[\pi
\]

Answer

Expert–verified

Hide Steps

Answer

$\boxed{f(x)=2x^{2}+8x+3}$ is the final answer.

Steps

Step 1 ：Given the function $f(x)=2(x+2)^{2}-5$.

Step 2 ：We need to rewrite it in the form $f(x)=a x^{2}+b x+c$.

Step 3 ：First, expand the expression $(x+2)^2$ to get $x^2 + 4x + 4$.

Step 4 ：Then, multiply this by 2 to get $2x^2 + 8x + 8$.

Step 5 ：Finally, subtract 5 from this to get $2x^2 + 8x + 3$.

Step 6 ：So, the function $f(x)=2(x+2)^{2}-5$ can be rewritten in the form $f(x)=a x^{2}+b x+c$ as $f(x)=2x^{2}+8x+3$.

Step 7 ：$\boxed{f(x)=2x^{2}+8x+3}$ is the final answer.