P.1 – Graphs & Models You will be able to… Sketch the graph of an equation Find intercepts of a graph Test a graph for symmetry Find the points of intersection of two graphs Interpret Mathematical models for real-life data

A) Graphing - Table of Values (plotting points): ex. 𝑦= 𝑥 2 −2 Intercepts: x-intercept (y = 0) and y-intercept (x = 0) ex. 2𝑥 −3𝑦=6 x yy -1 2 1

Graphing continued… Symmetry: 1) y-axis: replace x with (-x)  yields equivalent eqn. 2) x-axis: replace y with (-y)  yields equivalent eqn. 3) origin: replace x & y with (-x) & (-x) yields equivalent eqn. Transformations: To be discussed in P.3

B) Points of Intersection - What does it mean when two graphs intersect? ex. What does it mean that the equations 𝑦=3𝑥 −1 𝑎𝑛𝑑 𝑦= 1 2 𝑥+4 intersect at (2,5)? To find the intersection of 2 or more graphs is called solving a System of Equations.

Solving Systems Algebraically - Ex. Solve algebraically: 𝑥 2 −𝑦=3 𝑥 −𝑦=1

C) Mathematical Models - Calculus p.7 , example 6

Guided Practice - Page 8 #10, 56, 58, 66 Writing Practice (Challenge) – Write the equation of a polynomial whose x-intercepts are at -4 , 3, and 8 and whose end behavior is rises to the left and decreases to the right.