Answer:
Step-by-step explanation:
Start by factoring out 4 from the first two terms:
h(x) = 4(x^2 - 9x ) + 81
The coefficient of the x term is -9. Halve that, obtaining -9/2, and then square this result: (-9/2)^2 = 81/4. Then we have:
h(x) = 4(x^2 - 9x +81/4 -81/4 ) + 81
Now rewrite this trinomial as (x - 9/2)^2 and replace x^2 - 9x +81/4 by (x - 9/2)^2:
h(x) = 4( [x - 9/2]^2 -81/4 ) + 81
Performing the indicated multiplication, we get
h(x) = 4[x - 9/2)^2] - 81 + 81, or
h(x) = 4(x - 9/2)^2
