H(x) = x2 + 3x – 18

Rewrite the function by completing the square

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

Step-by-step explanation:

h(x) = x^2 + 3x – 18 (note the required use of " ^ " to indicate exponentiation)

Here 3 is the coefficient of the x term.  Take half of this 3 and square the result:  (3/2)^2 = 9/4.

Going back to h(x) = x^2 + 3x                       – 18

Add 9/4 and then subtract 9/4:

                        h(x) = x^2 + 3x + 9/4      - 9/4                       – 18

Rewrite this as  h(x) = (x + 3/2)^2 - 9/4 - 18, or

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

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hope this !