Question

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

Answer 1

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}`