Rewrite the function by completing the square. {:[g(x)=x^(2)-x-6],[g(x)=◻(x+◻)^(2)+◻]:}

Question

Rewrite the function by completing the square.  {:[g(x)=x^(2)-x-6],[g(x)=◻(x+◻)^(2)+◻]:}

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Identify Coefficients: Identify the coefficients of the x^2 and x terms in the quadratic function. The coefficient of x^2 is 1, and the coefficient of x is -1. We will use these to complete the square.Divide and Square: Divide the coefficient of the x term by 2 and square the result to find the number to complete the square. The coefficient of x is -1, so we divide it by 2 to get -1/2, and then square (-1/2) to get 1/4.Add and Subtract: Add and subtract the squared number inside the function to complete the square. We add and subtract (1/4) inside the function to maintain the equality. g(x) = x^2 - x + (1/4) - (1/4) - 6Rewrite as Perfect Square: Rewrite the quadratic part of the function as a perfect square. The quadratic part of the function is now x^2 - x + (1/4), which can be written as (x - 1/2)^2 because (x - 1/2)(x - 1/2) = x^2 - x + 1/4. g(x) = (x - 1/2)^2 - (1/4) - 6Combine Constants: Combine the constants outside the perfect square. Combine -1/4 and -6 to get -6 - 1/4 = -24/4 - 1/4 = -25/4. g(x) = (x - 1/2)^2 - 25/4Final Form: Write the final form of the function by completing the square. The completed square form of the function is g(x) = (x - 1/2)^2 - 25/4.

Rewrite the function by completing the square. $\newline$ $\begin{array}{l} g(x)=x^{2}-x-6 \\ g(x)=\square(x+\square)^{2}+\square \end{array}$

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Rewrite the function by completing the square.\newlineg(x)=x2−x−6g(x)=□(x+□)2+□ \begin{array}{l} g(x)=x^{2}-x-6 \\ g(x)=\square(x+\square)^{2}+\square \end{array} g(x)=x2−x−6g(x)=□(x+□)2+□​

Rewrite the function by completing the square. $\newline$ $\begin{array}{l} g(x)=x^{2}-x-6 \\ g(x)=\square(x+\square)^{2}+\square \end{array}$