{ Chapter 1: Functions and their Graphs 1.1 Rectangular Coordinates and 1.2 Graphs of Equations

 You know what this is already… 1.1 Rectangular Coordinates I. The Cartesian Plane 1.1 Rectangular Coordinates I. The Cartesian Plane

II. The Pythagorean Theorem and the Distance Formula

Find the distance between (2, -5) and (8, 3).

Show that the points (1, -3), (3, 2), and (-2, 4) form an isosceles triangle.

 The midpoint between two generic points can be found by taking the average of the x-coordinates and the average of the y-coordinates…  Find the midpoint of the line segment joining the points (-9, 5) and (4, 2) III. The Midpoint Formula

 “A solution of an equation in two variables (x and y) is an ordered pair (call it (a, b) ) such that when x is replaced with a and y replaced by b, the resulting equation is a true statement….”  WHAT? Basically, if the point fits into the equation, then that point should be included in the graph of the equation.  The actual graph is the set of ALL points that work. 1.2 Graphs of Equations I. The Graph of an Equation

 Sketch the graph of the following:  y= 2x+1 WHEN IN DOUBT PLOT (KINDA) RANDOM POINTS

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 X- Intercept Y-intercept How do you find them? II. Intercepts of a Graph

 Find the x and y intercept of:

 III. Symmetry

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 A circle with a center (h, k) and a radius r consists of all points (x, y) equidistant from the center. We can find the equation of a circle from what we know of the distance formula…  Find the standard form of the equation of a circle with center at (2, -5) and a radius of 4. IV. Circles