Linear, Quadratic, & Absolute Value Graphs with Translations COMMON CORE STATE STANDARDS HSF-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. HSF-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. HSF-IF.C.7b Graph piecewise-defined functions, including step functions and absolute value functions.

Graphing Linear Equations Slope-Intercept Form: Y = mx + b m = slope b = y-intercept Standard Form: Ax + By = C A and B are not both zero, C is a constant. Vertex Form Horizontal Lines: Y = C Vertical Lines: X = C (h,k) is the starting point a is the slope Examples: (1.) Domain: all real #’s Range: * Slope = ½ * * Y-Int. = 1

Graphing Quadratic Equations Vertex Form: Vertex: (h, k) Ratio of slopes (1,3,5) a=1 (1/1, 3/1, 5/1) a=2 (2/1, 6/1,10/1) a=3 (3/1, 9/1, 15/1) Axis of Symmetry: x = h Direction: a a = positive (up) a = negative (down)

Example: “Graph” Vertex: (-2,-3) Direction: Up Initial Slope: 1 (a=1) Domain: All real #’s Range: All real #’s -3. Ratio when a=1 (1/1, 3/1, 5/1)

* * Absolute Value Graphs: Shape “V ” Direction (a) a = positive (up) a = negative (down) Line of symmetry: x = h Vertex (h,k) x = h (h,k) * a = neg a = pos * (h,k) x = h

Vertex (h, k) =___________ Direction (a) = __________ Slope (+ & - a) = ________ Line of Symmetry = ______ (0,2) -1, down X = 0 Choose Points: Domain: All Real #’s. Range: All Real #’s 2