Graphing Absolute Functions

Slides:

Advertisements

Similar presentations

3.5 Absolute Value Functions

Advertisements

Graphing Absolute Value Functions Section 2.6 in your textbook.

Warm Up Find the solutions for each absolute value equation:

Introduction to Absolute Value Expressions and Graphs.

Example – Graph the solution set of Turn on your calculator and enter the Y= menu and enter the first part of the inequality Be sure to put the 2/5 in.

Graphs of Quadratic Functions In addition to level 3, students make connections to other content areas and/or contextual situations outside of.

Solving Absolute Value Equations Graphically Recall the steps used to solve an equation graphically: 1) Move all terms to the left hand side of the equation.

Graphing Absolute Value Equations. Absolute Value Equation A V-shaped graph that points upward or downward is the graph of an absolute value equation.

2.8 Absolute Value Functions p Absolute Value is defined by:

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.

Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a linear equation.

Graphing Quadratic Functions

Is this relation a function? Explain. {(0, 5), (1, 6), (2, 4), (3, 7)} Draw arrows from the domain values to their range values.

Section 5-3 Function Rules, Tables, and Graphs SPI 22H: select the linear graph that models the real-world situation SPI 52A: choose the matching linear.

Unit 7: Non-Linear Equations & Real- World Applications Section 1: Compound Interest Using 5x³: 5 is the coefficient, x is the base, 3 is the exponent.

Graphing absolute value functions and transformations

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.

 Absolute Value Functions!! Day One Should we do this later? No, DO NOW Complete the Absolute Value Exploration Sheet with a Pal.

1. Graph this piecewise function. f(x) = 3x – 1if x < -2 ½x + 1if x > Write an equation for this piecewise function. { Algebra II 1.

Graphing Quadratic Equations

Chapter 10.1 Notes: Graph y = ax 2 + c Goal: You will graph simple quadratic functions.

Graphing Quadratic Functions

6-5B Graphing Absolute Value Equations Algebra 1 Glencoe McGraw-HillLinda Stamper.

GRAPHING QUADRATIC FUNCTIONS

To find the x coordinate of the vertex, use the equation Then substitute the value of x back into the equation of the parabola and solve for y. You are.

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.

2.8 Absolute Value Functions

Graphing Quadratic Equations Using Vertex form Vertex Form of a Quadratic Function: A quadratic function with vertex at (h, k) can be written as:

Graphing Absolute Value Equations How do I make one of those V graphs?

Learning Task/Big Idea: Students will learn how to graph quadratic equations by binding the vertex and whether the parabola opens up or down.

A little review… In addition to level 3.0 and beyond what was taught in class, the student may:  Make connection with other concepts in math.

9.1 – Graphing Quadratic Functions. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5.

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

6.8 Graphing the Absolute Value. 6.8 – Graphing Absolute Value Goals / “I can…”  Translate the graph of an absolute value equation.

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,

Graphing Linear Equations 4.2 Objective 1 – Graph a linear equation using a table or a list of values Objective 2 – Graph horizontal or vertical lines.

Quadratic Functions A quadratic function is described by an equation of the following form: ax² + bx + c, where a ≠ 0 The graphs of quadratic functions.

Bellringer. Section 2.5 Absolute Value Equations and Graphs Obj: find domain, range and graph absolute value.

Function Tables and Graphs. Function A function is when each input (x-value) corresponds to exactly one output (y- value) In other words, when you substitute.

10-2 Graphing Quadratic Functions. Quadratic Functions (y = ax 2 +bx+c) When a is positive, When a is negative, When c is positive When c is negative.

Solving Absolute Value Equations & Inequalities Solving Absolute Value Equations & Inequalities.

Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a linear equation.

Coefficients a, b, and c are coefficients Examples: Find a, b, and c.

Graphing Absolute Value Functions

Do Now 10/09/2015 Solve given equations..

2.8 Graphing Absolute Value Functions

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.

Tables and Relations Review

Objective The student will be able to:

Graph Absolute Value Equations

Tables and Relations Review

Pre-Calculus 11: Section: 8.1 Solving Systems of Equation by Graphing

Absolute Value is defined by:

GRAPHING QUADRATIC FUNCTIONS

X- and y- intercepts.

Write Equations of Lines

Tables and Relations Review

Tables and Relations Review

CHAPTER TWO: LINEAR EQUATIONS AND FUNCTIONS

7.2 Graphing Equations Objectives:

7.2 Graphing Equations.

Solutions of Linear Functions

Graphing Absolute Value Functions

Warm up Solve and graph on number line 5|x+2| - 3 < 17

Section 2-6: Special Functions

Presentation transcript:

2.5-2.6 Graphing Absolute Functions

Complete the table and graph the points y = l x l x y -2 -1 1 2

Complete the table and graph the points y = l x – 2l + 3 x y 1 2 3 4

Vertex Form y = alx – hl + k (h, k) is the vertex of the “V” (if the sign doesn’t match the coordinate is negative) Identify the vertex y = Ix + 3I – 1 y = Ix – 5I + 6 y = Ix + 4I + 3

Graphing Absolute Value Identify and plot the vertex and decide whether the graph opens up or down. Set up a table of values Pick x-values on both sides of you vertex Plot the points Connect with lines (should be a “V” shape)

- If a>1 then the graph is narrower than y=lxl -if a<1 the graph is wider than the graph of y=lxl -if a is negative the v opens down -if a is positive the v opens up (a is the + and - slope of the two sides of the graph)

Graph each absolute value function y = I x – 1I + 2 y =2 I x +3I – 1 y = - I x + 2I + 4

Graphing absolute value on the calculator “y=“ Clear out any equations Enter function in to y1= To use absolute value symbols: Math key, tab one to the right for “NUM” Abs( is the first item on the menu so hit enter.

Writing an absolute value function from a graph -substitute the vertex read off the graph for h and k solve for “a” by plugging in any point on the graph for x and y. -plug the value you find in for a into the equation. Ex.

Suppose you are playing air hockey on an 8”by 4” table Suppose you are playing air hockey on an 8”by 4” table. The starting point of the puck is at (1,2). You wish to bank the puck off the side of the table at (5,4)and score a goal which is located at (8,2). Write the absolute value equation that this situation represents and decide whether or not you will score the goal.

Absolute Value An exclusive restaurant is open from 3:00 pm until 10:00 pm. Each evening, the number of people served S increases steadily and then decreases according to the model Where t=0 represents 12:00 pm. Use your calculator to graph the function and find the vertex. Explain what each coordinate of the vertex represents.