Rewrite the function by completing the square.

h (x) = 4x2 - 36x + 81

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