Rewrite the function by completing the square. {:[h(x)=4x^(2)+4x+1],[h(x)=◻(x+◻)^(2)+◻]:}

Question

Rewrite the function by completing the square.  {:[h(x)=4x^(2)+4x+1],[h(x)=◻(x+◻)^(2)+◻]:}

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Identify coefficients: Identify the quadratic coefficient, linear coefficient, and constant term in the given quadratic function. h(x) = 4x^2 + 4x + 1 Quadratic coefficient (a) = 4 Linear coefficient (b) = 4 Constant term (c) = 1Factor out quadratic coefficient: Factor out the quadratic coefficient from the x^2 and x terms. h(x) = 4(x^2 + x) + 1Find value to complete the square: Divide the linear coefficient (from the factored form) by 2 and square the result to find the value to complete the square. Linear coefficient in factored form = 1 (after factoring out 4) (1/2)^2 = 1/4Complete the square: Add and subtract the value found in the previous step inside the parentheses to complete the square. h(x) = 4(x^2 + x + 1/4 - 1/4) + 1Combine completed square terms: Combine the terms inside the parentheses that complete the square and the term that was subtracted. h(x) = 4((x + 1/2)^2 - 1/4) + 1Distribute quadratic coefficient: Distribute the quadratic coefficient (4) to the terms inside the parentheses. h(x) = 4(x + 1/2)^2 - 4(1/4) + 1Simplify constant terms: Simplify the constant terms. -4(1/4) + 1 = -1 + 1 = 0 h(x) = 4(x + 1/2)^2 + 0Write in completed square form: Since adding 0 does not change the value, we can write the function in its completed square form. h(x) = 4(x + 1/2)^2

Rewrite the function by completing the square. $\newline$ $\begin{array}{l} h(x)=4 x^{2}+4 x+1 \\ h(x)=\square(x+\square)^{2}+\square \end{array}$

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Rewrite the function by completing the square.\newlineh(x)=4x2+4x+1h(x)=□(x+□)2+□ \begin{array}{l} h(x)=4 x^{2}+4 x+1 \\ h(x)=\square(x+\square)^{2}+\square \end{array} h(x)=4x2+4x+1h(x)=□(x+□)2+□​

Rewrite the function by completing the square. $\newline$ $\begin{array}{l} h(x)=4 x^{2}+4 x+1 \\ h(x)=\square(x+\square)^{2}+\square \end{array}$