2.8 Absolute Value Functions p. 122. Absolute Value is defined by:

Slides:



Advertisements
Similar presentations
5-3 Transforming parabolas
Advertisements

Think, Think, Think. Algebra I Seminar. How Much Do you Remember? The Coordinate Plane X-axis, Y-axis Slope Y-intercept Ordered Pairs Slope Intercept.
Calculating Slope of a Line :
Graphing Linear Equations In Slope-Intercept Form.
Graphing Using Slope - Intercept STEPS : 1. Equation must be in y = mx + b form 2. Plot your y – intercept ( 0, y ) 3. Using your y – intercept as a starting.
Absolute Value is defined by: The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x.
13.2 Solving Quadratic Equations by Graphing CORD Math Mrs. Spitz Spring 2007.
1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.
Warm Up Find: f(0) = f(2) = f(3) = f(4) =.
Graphing Absolute Functions
3.2 Graphing Functions and Relations
Graphing absolute value functions and transformations
Apply rules for transformations by graphing absolute value functions.
Writing equations given a point and the slope of a line
2.8 : Absolute Value Functions What is absolute value? What does the graph of an absolute value function look like? How do you translate an absolute value.
Graph Absolute Value Functions using Transformations
Absolute Value Functions What is an absolute value function? How is an absolute value graph graphed, written, and interpreted?
 Absolute Value Functions!! Day One Should we do this later? No, DO NOW Complete the Absolute Value Exploration Sheet with a Pal.
Standard MM2A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions. b. Investigate and explain.
1. Graph this piecewise function. f(x) = 3x – 1if x < -2 ½x + 1if x > Write an equation for this piecewise function. { Algebra II 1.
W ARM UP ( REVIEW ). 9x-9y> P IECEWISE F UNCTIONS.
3.1 Symmetry; Graphing Key Equations. Symmetry A graph is said to be symmetric with respect to the x-axis if for every point (x,y) on the graph, the point.
Graphing Quadratic Equations
6-5B Graphing Absolute Value Equations Algebra 1 Glencoe McGraw-HillLinda Stamper.
GRAPHING QUADRATIC FUNCTIONS
Graphing Absolute Value Functions using Transformations.
1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.
Do Now Write the slope-intercept equation of this line.
Graphing Absolute Value Equations How do I make one of those V graphs?
6.6 Analyzing Graphs of Quadratic Functions. The vertex form of a quadratic function gives us certain information that makes it very easy to graph the.
QUADRATIC EQUATIONS in VERTEX FORM y = a(b(x – h)) 2 + k.
Notes Over 2.8 Graphing an Absolute Value Function xy Vertex: Axis of Symmetry: Slope: ( 1, 2 ) x = 1 up 2, right/left.
What you will learn today
Algebra I Algebraic Connections Algebra II Absolute Value Functions and Graphs.
2.8 Absolute Value Functions Goals:1. Representing absolute value functions 2. Using absolute value functions in real life Given how do you find the vertex,
MM2A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions. b. Investigate and explain characteristics.
Bellringer. Section 2.5 Absolute Value Equations and Graphs Obj: find domain, range and graph absolute value.
3.2 Graphing Quadratic Functions in Vertex or Intercept Form Definitions Definitions 3 Forms 3 Forms Steps for graphing each form Steps for graphing each.
4.2A Graph Quadratic Functions in Vertex or Intercept Form Algebra II Algebra II.
Evaluate the expression for x = -6 1)|x|2) - | x – 3 | 3) | 1 – x | + 44) -3 | x + 4 | – Warm - up.
How To Graph Quadratic Equations Standard Form.
Graphing Absolute Value Functions
Do Now 10/09/2015 Solve given equations..
2.8 Graphing Absolute Value Functions
2-7 Absolute Value Functions and Graphs
Graph Absolute Value Functions using Transformations
Graph Absolute Value Functions using Transformations
1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.
How to Graph Quadratic Equations
How To Graph Quadratic Equations
Graphing Absolute Value Functions
Graph Absolute Value Functions using Transformations
2-6 Special Functions.
Graph Absolute Value Functions using Transformations
2.7 Use Absolute Value Functions and Transformations
Absolute Value is defined by:
GRAPHING QUADRATIC FUNCTIONS
4.10 Write Quadratic Functions and Models
3.1 Notes: Solving Systems of Equations
How To Graph Quadratic Equations.
Graphing Absolute Value Functions
How To Graph Quadratic Equations.
CHAPTER TWO: LINEAR EQUATIONS AND FUNCTIONS
Section 10.2 “Graph y = ax² + bx + c”
7.2 Graphing Equations.
Chapter 2.8! By: Hannah Murphy.
Warm up Solve and graph on number line 5|x+2| - 3 < 17
Graphing Quadratic Functions
Write Quadratic Functions and Models
How To Graph Quadratic Equations.
Presentation transcript:

2.8 Absolute Value Functions p. 122

Absolute Value is defined by:

The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x To the right of x = 0 the line is y = x Notice that the graph is symmetric in the y-axis because every point (x,y) on the graph, the point (-x,y) is also on it.

y = a |x - h| + k Vertex (h,k) & is symmetrical in the line x=h V-shaped If a< 0 the graph opens down (a is negative) If a>0 the graph opens up (a is positive) The graph is wider if |a| < 1 (fraction < 1) The graph is narrower if |a| > 1 a is the slope to the right of the vertex (…-a is the slope to the left of the vertex)

To graph y = a |x - h| + k 1.Plot the vertex (h,k) (set what’s in the absolute value symbols to 0 and solve for x; gives you the x-coord. of the vertex, y-coord. is k.) 2.Use the slope to plot another point to the RIGHT of the vertex. 3.Use symmetry to plot a 3 rd point 4.Complete the graph

Graph y = -|x + 2| V = (-2,3) 2.Apply the slope a=-1 to that point 3.Use the line of symmetry x=-2 to plot the 3rd point. 4.Complete the graph

Graph y = -|x - 1| + 1

Write the equation for:

The vertex (0,-3) It has the form: y = a |x - 0| - 3 To find a: substitute the coordinate of a point (2,1) in and solve (or count the slope from the vertex to another point to the right) Remember: a is positive if the graph goes up a is negative if the graph goes down So the equation is: y = 2|x| -3

Write the equation for: y = ½|x| + 3

Assignment