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