SAMPLE College Algebra

1.1 Graphs 17 If one is looking down at a city grid, or a forest, or a park, in the same way one could tell someone to walk forward, or backwards. One could tell someone to walk to the left, or the right. First, a starting point needs to be clear. In a coordinate plane, the starting point is the center, and it is called the origin. The origin is shown in the graph below, with a red dot. Solved Problem 1.1 Graph the coordinate pairs (4, 2), (2, 4), (-4, -2), and (-2, -4) • (4, 2) From the origin go 4 to the right and 2 up, shown with a green dot • (2, 4) From the origin go 2 to the right and 4 up, shown with a blue dot • (-2, -4) From the origin go 2 to the left and 4 down, shown with a yellow dot − 4 − 2 2 4 2 4 x y Final Answer For the coordinate pair ( 4 , 2), shown with a green dot, the x-coordinate is 4. For the same coordinate pair (4, 2 ), shown with a green dot, the y-coordinate is 2. ■ Coordinate pairs, seem like a simple concept. In an algebra course, it might be assumed that a student already knows this. To plot coordinates (0,0) in red, from the center or origin, go 0 units to the right, and 0 units up. This is shown in the graph below with a red point. To plot coordinates (1,1) in blue, − 4 − 2

from the origin, go 1 unit to the right, and 1 unit up • Plot coordinates (2,4) in green. From the origin, go 2 units to the right, and 4 units up • Plot coordinates (-1,1) in black. From the origin, go 1 unit to the left, and 1 unit up • Plot coordinates (-2,4) in yellow. From the origin, go 2 units to the left, and 4 units up • Notice that a shape is forming, kind of like a cup If additional points are plotted, then a curved line will form, as shown in the blue line, in the graph to the right. This blue curve, that looks kind of like a letter U or a cup, is a special curve called a parabola . The point here is to review graphs. A parabola will be discussed again in detail

2 4 6

y

x

4 − 2

2 4

−

− 2

2 4 6

y

x

− 4 − 2

2 4

− 2