Answer:
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
