Question

medal and fan for best answer :):):):):)


in the function f(x)=4(x^2-6x+ ) +20 what number belongs in the blank to complete the square?

Answer 1

(-6/2)^2=9

Answer 2

The already-completed square will look like this: \(4 (x - a)^2 + 20 \)
Let's just look at the smaller picture though.
\( (x - a)^2 \)
If we expand that form, we get: \(x^2 - 2a x + a^2 = x^ 2 - 6x + \_\_ \)

Notice the -2a x and the -6x are corresponding terms. So -2a = -6.
Then the blank corresponds with our a^ 2 part. In total, our general process is dividing the x-coefficient by 2 (a = -6/-2) and then squaring the result. (a^ 2)

Answer 3

** side note: do not be confused by the division by -2 vs. 2, we simply square the result to remove the sign entirely.

Answer 4

is the answer 9?

Answer 5

Yes. :)