Rewrite each relation in the form y = a(x-h)2 + k by completing the square, then state the vertex. y = -2x^2 – 12x - 7

Explanation:

h = b/2a

h= -12/2(-2)

h= -12/-4

h= 3

k = 4ac - b^2/ 4a

k = 4(-2)(-7) - (-12)^2/ 4(-2)

k = 56 - 144 / -8

k = -88 / -8

k = 11

y = -2x^2 - 12x - 7 in the form a(x-h)^2 + k

= -2(x + 3)^2 + 11

vertex = (h,k)

therefore the vertex is 3 and 11

the first historical instance of china engaging in internationalism was during the han dynasty.[1] at the start of the han dynasty, the huns in the north were attacking the frontiers of han and trying to obtain riches. emperor wu of han wanted to gain an alliance with a country called dayuezhi so the two countries could join together and fight against the huns.[2] to obtain this alliance, emperor wu sent zhang qian to the west to establish economic and cultural connections.[2] history records that during the han dynasty there were four primary avenues of contact between china and europe. they included the northern land route, the central land route, the southern sea route, and the far southern sea route.[1] the most famous of these routes is the central land route, or the classical silk road, comprising a network of roads stretching from northwest china to the ports of syria and the black sea, which passed through the oasis of the turkestans and northern persia.[1] the silk road was significant for chinese emperors because it provided dominance over central asia by developing resources and provided new markets for the export of china's most valuable resources.[1]

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