Question

I need help on this!!

Answer 1

1, -0.5, -6.25

Explanation:

The number in the left box is the leading coefficient. The coefficient of x^2 is 1, so that goes in the first box.

__

The number in the second box is half the coefficient of x, divided by the leading coefficient:

(1/2)(-1)/1 = -1/2

__

The number in the third box (k) is the number required to make the rewritten g(x) match the original g(x). So far, we have ...

g(x) = 1(x -1/2)^2 + k = x^2 -x -6

x^2 -x +1/4 +k = x^2 -x -6 . . . . . expand the square

1/4 +k = -6 . . . . . . . . . . . . . . . . . subtract the x-terms from both sides

k = -6 1/4 . . . . . . . . . . . . . . . . . . subtract 1/4

So, you have ...

`g(x)=\boxed{1}(x+\boxed{-0.5})^2+\boxed{-6.25}`