Rewrite the function by completing the square. {:[h(x)=2x^(2)+11 x+15],[h(x)=◻(x+◻)^(2)+◻]:}

Question

Rewrite the function by completing the square.  {:[h(x)=2x^(2)+11 x+15],[h(x)=◻(x+◻)^(2)+◻]:}

Bytelearn · Accepted Answer

Identify coefficient of x^2: Identify the coefficient of x^2, which is 2, and factor it out from the x terms. h(x) = 2(x^2 + (11/2)x) + 15Complete the square: To complete the square, we need to add and subtract the square of half the coefficient of x inside the parentheses. The coefficient of x is 11/2, so half of that is 11/4. Squaring 11/4 gives us (11/4)^2 = 121/16. h(x) = 2(x^2 + (11/2)x + 121/16 - 121/16) + 15Add and subtract: Add and subtract 121/16 inside the parentheses, but remember to multiply the subtracted term by 2 because we factored 2 out in the first step. h(x) = 2(x^2 + (11/2)x + 121/16) - 2(121/16) + 15Simplify the equation: Simplify the equation by combining like terms outside the parentheses. h(x) = 2(x + 11/4)^2 - 2(121/16) + 15 h(x) = 2(x + 11/4)^2 - 121/8 + 15Convert 15 to fraction: Convert 15 to a fraction with a denominator of 8 to combine with -121/8. 15 = 120/8 h(x) = 2(x + 11/4)^2 - 121/8 + 120/8Combine the fractions: Combine the fractions. h(x) = 2(x + 11/4)^2 - 1/8Write final completed square form: Write the final completed square form of the function. h(x) = 2(x + 11/4)^2 - 1/8

Rewrite the function by completing the square. $\newline$ $\begin{array}{l} h(x)=2 x^{2}+11 x+15 \\ h(x)=\square(x+\square)^{2}+\square \end{array}$

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Rewrite the function by completing the square.\newlineh(x)=2x2+11x+15h(x)=□(x+□)2+□ \begin{array}{l} h(x)=2 x^{2}+11 x+15 \\ h(x)=\square(x+\square)^{2}+\square \end{array} h(x)=2x2+11x+15h(x)=□(x+□)2+□​

Rewrite the function by completing the square. $\newline$ $\begin{array}{l} h(x)=2 x^{2}+11 x+15 \\ h(x)=\square(x+\square)^{2}+\square \end{array}$