Rewrite the function by completing the square. {:[g(x)=4x^(2)-16 x+7],[g(x)=◻(x+◻)^(2)+◻]:}

Question

Rewrite the function by completing the square.  {:[g(x)=4x^(2)-16 x+7],[g(x)=◻(x+◻)^(2)+◻]:}

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Identify coefficients: Identify the quadratic coefficient, linear coefficient, and constant term in the given quadratic function. g(x) = 4x^2 - 16x + 7 Quadratic coefficient (a) = 4 Linear coefficient (b) = -16 Constant term (c) = 7Factor out quadratic coefficient: Factor out the quadratic coefficient from the x^2 and x terms. g(x) = 4(x^2 - 4x) + 7Find value to complete the square: Find the value to complete the square. This is done by taking half of the coefficient of x (after factoring out the quadratic coefficient) and squaring it. Half of the coefficient of x is -4/2 = -2. Squaring this value gives (-2)^2 = 4.Add and subtract to complete the square: Add and subtract the value found in the previous step inside the parentheses to complete the square. Remember to balance the equation by adding the same value outside the parentheses, multiplied by the quadratic coefficient. g(x) = 4(x^2 - 4x + 4 - 4) + 7 To balance the equation, we add 4 * 4 = 16 to the constant term. g(x) = 4(x^2 - 4x + 4) - 16 + 7Combine constant terms: Combine the constant terms outside the parentheses. g(x) = 4(x^2 - 4x + 4) - 9Write as perfect square: Write the trinomial as a perfect square. g(x) = 4(x - 2)^2 - 9

Rewrite the function by completing the square. $\newline$ $\begin{array}{l} g(x)=4 x^{2}-16 x+7 \\ g(x)=\square(x+\square)^{2}+\square \end{array}$

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Rewrite the function by completing the square.\newlineg(x)=4x2−16x+7g(x)=□(x+□)2+□ \begin{array}{l} g(x)=4 x^{2}-16 x+7 \\ g(x)=\square(x+\square)^{2}+\square \end{array} g(x)=4x2−16x+7g(x)=□(x+□)2+□​

Rewrite the function by completing the square. $\newline$ $\begin{array}{l} g(x)=4 x^{2}-16 x+7 \\ g(x)=\square(x+\square)^{2}+\square \end{array}$