Rewrite the function by completing the square. {:[f(x)=4x^(2)+12 x+9],[f(x)=◻(x+◻)^(2)+◻]:}

Question

Rewrite the function by completing the square.  {:[f(x)=4x^(2)+12 x+9],[f(x)=◻(x+◻)^(2)+◻]:}

Bytelearn · Accepted Answer

Identify coefficients: Identify the quadratic and linear coefficients in the original function. The original function is f(x) = 4x^2 + 12x + 9. The quadratic coefficient (the coefficient of x^2) is 4, and the linear coefficient (the coefficient of x) is 12.Factor out quadratic coefficient: Factor out the quadratic coefficient from the x^2 and x terms. To complete the square, we need to factor out the quadratic coefficient from the x^2 and x terms. This gives us: f(x) = 4(x^2 + 3x) + 9.Find completion value: Find the value to complete the square. To complete the square for the expression x^2 + 3x, we need to add and subtract (b/2a)^2, where a is the coefficient of x^2 (which is 1 after factoring out the 4) and b is the coefficient of x (which is 3). So we calculate (3/2*1)^2 = (3/2)^2 = 9/4.Add and subtract value: Add and subtract the value found inside the parentheses. We add and subtract 9/4 inside the parentheses to complete the square: f(x) = 4(x^2 + 3x + 9/4 - 9/4) + 9.Write perfect square trinomial: Write the perfect square trinomial and adjust the constant term. The expression x^2 + 3x + 9/4 is a perfect square trinomial, which can be written as (x + 3/2)^2. We also need to subtract the 9/4 that we added inside the parentheses, but since it's multiplied by 4, we subtract 4*(9/4) from the constant term: f(x) = 4(x + 3/2)^2 - 4*(9/4) + 9.Adjust constant term: Simplify the constant term. Now we simplify the constant term by subtracting 4*(9/4) from 9: f(x) = 4(x + 3/2)^2 - 9 + 9. f(x) = 4(x + 3/2)^2 + 0.Simplify constant term: Write the final form of the function. The function is now written in the form of a completed square: f(x) = 4(x + 3/2)^2.

Rewrite the function by completing the square. $\newline$ $\begin{array}{l} f(x)=4 x^{2}+12 x+9 \\ f(x)=\square(x+\square)^{2}+\square \end{array}$

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Rewrite the function by completing the square.\newlinef(x)=4x2+12x+9f(x)=□(x+□)2+□ \begin{array}{l} f(x)=4 x^{2}+12 x+9 \\ f(x)=\square(x+\square)^{2}+\square \end{array} f(x)=4x2+12x+9f(x)=□(x+□)2+□​

Rewrite the function by completing the square. $\newline$ $\begin{array}{l} f(x)=4 x^{2}+12 x+9 \\ f(x)=\square(x+\square)^{2}+\square \end{array}$