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

$f (x) = 2 x^{2} + 8 x + 3$ 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 $x^{2} + 4 x + 4$ .

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

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

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 $f (x) = 2 x^{2} + 8 x + 3$ .

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