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

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step-by-step explanation: