Question

Please use picture for the question not the writing

Answer 1

$\tt \: f(x) = {x}^{2} + 4x - 1$

To complete the square, the same value needs to be added to both sides

$\tt \: f(x) + ? = {x}^{2} + 4x + ? - 1$

To complete the square, Add 4 on both sides of the equation

$\tt \: f(x) + 4 = {x}^{2} + 4x + 4 - 1$

Use a²+2ab+b²=(a+b)² to factor the expression

$\tt \: f(x) + 4 = (x + 2)^{2} - 1$

Move the constant to the right-hand side and change its sign

$\tt \: f(x) = {(x + 2)}^{2} - 1 - 4$

Calculate the difference

$\tt \: f(x) = {(x + 2)}^{2} -5$

And, We are done solving!!~

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The option that corresponds our final answer is option D...