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Rewrite the function by completing the square.h(x)= x^2 +3 x -18

User Biswanath
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1 Answer

4 votes

The function is given as


h(x)=x^2+3x-18

Step 1: Divide the coefficient of x by 2 and square it then add to 3x and then subtract from -18


\begin{gathered} h(x)=x^2+3x-18 \\ h(x)=(x^2+3x)-18 \\ h(x)=(x^2+3x+((3)/(2))^2)-18-((3)/(2))^2 \end{gathered}

Step 2: Combine the squares and then simplify the fractions to decimal


\begin{gathered} h(x)=(x^2+3x+((3)/(2))^2)-18-((3)/(2))^2 \\ h(x)=(x^{}+(3)/(2))^2-18-(9)/(4) \\ h(x)=(x^{}+(3)/(2))^2-(18)/(1)-(9)/(4) \\ h(x)=(x^{}+(3)/(2))^2(-72-9)/(4) \\ h(x)=(x^{}+(3)/(2))^2-(81)/(4) \end{gathered}

Hence,

The final answer is


h(x)=(x^{}+(3)/(2))^2-(81)/(4)

In decimal, it can be written as


\begin{gathered} h(x)=(x^{}+1.5)^2-20.25 \\ \end{gathered}

User Kocus
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