1. 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.

2. 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

3. 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)

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

5. * * 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

6. 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