Respuesta :
The function is given as
[tex]h(x)=x^2+3x-18[/tex]Step 1: Divide the coefficient of x by 2 and square it then add to 3x and then subtract from -18
[tex]\begin{gathered} h(x)=x^2+3x-18 \\ h(x)=(x^2+3x)-18 \\ h(x)=(x^2+3x+(\frac{3}{2})^2)-18-(\frac{3}{2})^2 \end{gathered}[/tex]Step 2: Combine the squares and then simplify the fractions to decimal
[tex]\begin{gathered} h(x)=(x^2+3x+(\frac{3}{2})^2)-18-(\frac{3}{2})^2 \\ h(x)=(x^{}+\frac{3}{2})^2-18-\frac{9}{4} \\ h(x)=(x^{}+\frac{3}{2})^2-\frac{18}{1}-\frac{9}{4} \\ h(x)=(x^{}+\frac{3}{2})^2\frac{-72-9}{4} \\ h(x)=(x^{}+\frac{3}{2})^2-\frac{81}{4} \end{gathered}[/tex]Hence,
The final answer is
[tex]h(x)=(x^{}+\frac{3}{2})^2-\frac{81}{4}[/tex]In decimal, it can be written as
[tex]\begin{gathered} h(x)=(x^{}+1.5)^2-20.25 \\ \end{gathered}[/tex]