Question

Rewrite the function by completing the square.

h(x) = 41²

361 +81

Answer 1

Answer:

h(x) = (41+9)^2 - 377

Step-by-step explanation:

You have the following expression:

$h(x)=41^2+361+81$

to complete the square you need that the third term is a squared of another number. In this case 9^2 = 81.

Furthermore, it is necessary that the second term is twice the product between the square root of the first term and the square root of the third term. That is, the second term must be 2x41x9 = 738

Then, you can sum 377 unit to 361 in order to complete the square. But also you have to subtract 377:

$h(x)=41^2+361+9^2\\\\h(x)=(41^2+361+377+9^2)-377\\\\h(x)=(41+738+9^2)-377\\\\h(x)=(41+9)^2-377$

hence, the function can be writen as:

h(x) = (41+9)^2 - 377