The graph of a quadratic function touches, but does not cross the x-axis at x = 4 Which function represents this
Situation?
Py=x2-16
y=x2 - 4x
y 2 -8x + 16
y=x2 + 8x + 16

americans began to notice growing differences between the northern and southern sections of the country. there were more people living in cities in the north, which made it more urban. more people lived on farms in the south, which made it more rural. while many people were farmers in the northern states, there were now other ways to make a living, such as working in mechanical cotton gins factories manufacturing cloth, tools and other goods. people in the north supported high tariffs on goods imported from europe because the extra cost encouraged people to “buy american” instead. in the southern states, planters did not like tariffs because they sold most of their production to europe and bought their tools from there as well. southerners believed the protective tariff was something that only northern factory owners keep their profits high. so the southern politicians came up with an idea. they would opt out. they would simply ignore the protective tariff. it was ‘null and void’ in south carolina. the state would not collect the taxes on goods imported into south carolina, no matter what the president said they had to do. this decision led to the nullification crisis.

the elements of art are the visual tools that the artist uses to create a composition. these are line, shape, color, value, form, texture, and space.

the principles of art and design are balance, contrast, emphasis, movement, pattern, rhythm, and unity/variety.