Objective Introduce the Coordinate plane, the 11 parts of it, how to name coordinates and plot points.

x-axis y-axis The coordinate plane is formed by the intersection of two perpendicular number lines called axes. The point of intersection, called the origin, is at 0 on each number line. The horizontal number line is called the x-axis, and the vertical number line is called the y-axis. ORIGIN

The coordinate plane sectioned into 4 Quadrants The coordinate plane sectioned into 4 Quadrants. Starting in the upper right hand side, they are labeled Quadrant I, II, III, IV. Quadrant I Quadrant II Quadrant III Quadrant IV (+,+) (-,-) (-,+) (+,-) All the points in each Quadrant have something in common. How they are feeling in the morning and evening! They are either Happy (+) or Sad (-)

Points on the coordinate plane are described using ordered pairs Points on the coordinate plane are described using ordered pairs. An ordered pair consists of an x-coordinate and a y-coordinate and is written (x, y). The x-coordinate tells how many units to move left or right from the origin. The y-coordinate tells how many units to move up or down. Think about going to a PARTY! Reading Math ( x , y ) ( , )

Example 1: Graphing Points in the Coordinate Plane Graph each point. A. T(–4, 4) Start at the origin. T(–4, 4) • Move 4 units left and 4 units up. B. U(0, –5) Start at the origin. Move 5 units down. C. V (–2, –3) • V(–2, −3) Start at the origin. • U(0, –5) Move 2 units left and 3 units down.

Check It Out! Example 1 Graph each point. A. R(2, –3) Start at the origin. Move 2 units right and 3 units down. B. S(0, 2) Start at the origin. Move 2 units up. C. T(–2, 6) Start at the origin. Move 2 units left and 6 units up.

Look at the graph at the top of this lesson Look at the graph at the top of this lesson. The axes divide the coordinate plane into four quadrants. Points that lie on an axis are not in any quadrant.

Example 2: Locating Points in the Coordinate Plane Name the quadrant in which each point lies. •E •F •H •G y A. E Quadrant ll B. F no quadrant (y-axis) x C. G Quadrant l D. H Quadrant lll

Name the quadrant in which each point lies. Check It Out! Example 2 Name the quadrant in which each point lies. y A. T no quadrant (y-axis) •W •U •T B. U Quadrant l x C. V Quadrant lll •V D. W Quadrant ll

Graph each point. Name the quadrant in which each point lies. Lesson Quiz: Part 1 Graph each point. Name the quadrant in which each point lies. 1. (2, 0) None 2. (–3, –4) lll • 3. (1, –1) lV • • 4. (–5, 4) ll •

When you graph ordered pairs generated by a function, they may create a pattern.

Example 4A: Generating and Graphing Ordered Pairs Generate ordered pairs for the function using the given values for x. Graph the ordered pairs and describe the pattern. y = 2x + 1; x = –2, –1, 0, 1, 2 • Input Output Ordered Pair x y (x, y) –2 2(–2) + 1 = –3 (–2, –3) –1 2(–1) + 1 = –1 (–1, –1) 2(0) + 1 = 1 (0, 1) 1 2(1) + 1 = 3 (1, 3) 2(2) + 1 = 5 2 (2, 5) The points form a line.

Example 4B: Generating and Graphing Ordered Pairs y = x2 – 3; x = –2, –1, 0, 1, 2 Input Output Ordered Pair x y (x, y) –2 (–2)2 – 3 = 1 (–2, 1) –1 (–1)2 – 3 = –2 (–1, –2) (0)2 – 3 = –3 (0, –3) 1 (1)2 – 3 = –2 (1, –2) (2)2 – 3 = 1 2 (2, 1) The points form a U shape.

Example 4C: Generating and Graphing Ordered Pairs y = |x – 2|; x = 0, 1, 2, 3, 4 Input Output Ordered Pair x y (x, y) |0 – 2| = 2 (0, 2) 1 |1 – 2| = 1 (1, 1) 2 |2 – 2| = 0 (2, 0) 3 |3 – 2| = 1 (3, 1) 4 |4 – 2| = 2 (4, 2) The points form a V shape.

Input Output Ordered Pair Check It Out! Example 4a 1 2 y = x – 4; x = –4, –2, 0, 2, 4 Input Output Ordered Pair x y (x, y) –4 –2 – 4 = –6 (–4, –6) –2 –1 – 4 = –5 (–2, –5) 0 – 4 = –4 (0, –4) 2 1 – 4 = –3 (2, –3) 4 2 – 4 = –2 (4, –2) The points form a line.

Input Output Ordered Pair Check It Out! Example 4b y = 3x2 + 3; x = –3, –1, 0, 1, 3 Input Output Ordered Pair x y (x, y) –3 3(–3)2 + 3 = 30 (–3, 30) –1 3(–1)2 + 3 = 6 (–1, 6) 3(0)2 + 3 = 3 (0, 3) 1 3(1)2 + 3 = 6 (1, 6) 3(3)2 + 3 = 30 3 (3, 30) The points form a U shape.

Input Output Ordered Pair Check It Out! Example 4c y = |x – 2|; x = 0, 1, 2, 3, 4 Input Output Ordered Pair x y (x, y) |0 – 2| = 2 (0, 2) 1 |1 – 2| = 1 (1, 1) 2 |2 – 2| = 0 (2, 0) 3 |3 – 2| = 1 (3, 1) 4 |4 – 2| = 2 (4, 2) The points form a V shape.

The pattern is U-shaped. Lesson Quiz: Part 3 6. Generate ordered pairs for y = x² –5 using x = –2, –1, 0, 1, and 2. Graph the ordered pairs, and describe the pattern. • (–2, –1) (–1, –4) (0, –5) (1, –4) (2, –1) The pattern is U-shaped.