91Ó°ÊÓ

Graph each function using shifts of a parent function and a few characteristic points. Clearly state and indicate the transformations used and identify the location of all vertices, initial points, and/or inflection points. $$h(x)=-2(x+1)^{2}-3$$

Picks theorem is an interesting yet little known formula for computing the area of a polygon drawn in the Cartesian coordinate system. The formula can be applied as long as the vertices of the polygon are lattice points (both \(x\) and \(y\) are integers). If \(B\) represents the number of lattice points lying directly on the boundary of the polygon (including the vertices), and I represents the number of points in the interior, the area of the polygon is given by the formula shown. Use some graph paper to carefully draw a triangle with vertices at \((-3,1),(3,9),\) and (7, 6) then use Pick's theorem to compute the triangle's area.

Using the concept of slope, match each description with the graph that best illustrates it. Assume time is scaled on the horizontal axes, and height, speed, or distance from the origin (as the case may be) is scaled on the vertical axis. (GRAPH CAN'T COPY) I walked toward the candy machine, stared at it for a while then changed my mind and walked back.

Prison population: In \(1990,\) the number of persons sentenced and serving time in state and federal institutions was approximately \(740,000 .\) By the year \(2000,\) this figure had grown to nearly 1,320,000 (a) Find a linear equation with \(t=0\) corresponding to 1990 that models this data, (b) discuss the slope ratio in context, and (c) use the equation to estimate the prison population in 2007 if this trend continues.