P.1 Graphs and Models Main Ideas Sketch the graph of an equation. find the intercepts of a graph. Test a graph for symmetry with respect to an axis and the origin. Find the points of intersection of two graphs.

Graphing Equations There are several techniques you can use to graph any equation. 1.Plot points – most basic and difficult method 2.Graphing Calculator- fastest, but can not use on tests. 3.Knowing basic equations and transformations.

Graph without a calculator 1.y = ²/₅x y = 4 – x² 3.y = |x + 2| 4.y = √x – 4 5.y = 2/x

Intercepts of a graph Y-intercept(s) are located at (0,b). Find b by substituting zero into the equation for x and solve the equation for y. X-intercept(s) are located at (a,0). Find a by substituting zero into the equation for y and solve the equation for x. Do equations always have real intercepts? Therefore intercepts are aids in graphing an equation.

Find the x- and y-intercepts of the following graphs. 1. y = x² + x – 22. x²y – x² + 4y = 16

Symmetry of a graph Symmetry is helpful to know because you only need half as many points to graph. Symmetry about y-axis happens when x = -x in the equation. Points (x, y) and (-x, y) Symmetry about x-axis happens when y = -y in the equation. Points(x, y) and (x, -y) Symmetry about the origin happens when x = -x and y = -y in the equation. Points (x, y) and (-x, -y)

Test for symmetry. 1.y = x² y² = x³ - 4x 3.xy = 4 4.2x - 4y² = 12

Points of intersection Finding a value(s) that satisfy both equations. Solve equations by Graphing Substitution Elimination

Find the points of intersection 1.x + y = 22. x² + y² = 5 2x – y = 1 x – y = 1