Inequality Set Notation

Slides:

Advertisements

Similar presentations

Write equation or Describe Transformation. Write the effect on the graph of the parent function down 1 unit1 2 3 Stretch by a factor of 2 right 1 unit.

Advertisements

ParabolasParabolas by Dr. Carol A. Marinas. Transformation Shifts Tell me the following information about: f(x) = (x – 4) 2 – 3  What shape is the graph?

+ Translating Parabolas § By the end of today, you should be able to… 1. Use the vertex form of a quadratic function to graph a parabola. 2. Convert.

Warm-Up: you should be able to answer the following without the use of a calculator 2) Graph the following function and state the domain, range and axis.

The General Quadratic Function Students will be able to graph functions defined by the general quadratic equation.

Start- Up Day 11 1.Rewrite in slope-intercept form: 2.Describe the transformations as compared to the basic Absolute Value Graph:

Day 6 Pre Calculus. Objectives Review Parent Functions and their key characteristics Identify shifts of parent functions and graph Write the equation.

Family of Quadratic Functions Lesson 5.5a. General Form Quadratic functions have the standard form y = ax 2 + bx + c  a, b, and c are constants  a ≠

Section 4.1 – Quadratic Functions and Translations

Unit 1B quadratics Day 3. Graphing a Quadratic Function EQ: How do we graph a quadratic function that is in vertex form? M2 Unit 1B: Day 3 Lesson 3.1B.

Give the coordinate of the vertex of each function.

4-1 Quadratic Functions Unit Objectives: Solve a quadratic equation. Graph/Transform quadratic functions with/without a calculator Identify function.

Transformations of Functions. Graphs of Common Functions See Table 1.4, pg 184. Characteristics of Functions: 1.Domain 2.Range 3.Intervals where its increasing,

4.1 Quadratic Functions and Transformations A parabola is the graph of a quadratic function, which you can write in the form f(x) = ax 2 + bx + c, where.

Unit 1 part 2 Test Review Graphing Quadratics in Standard and Vertex Form.

Warm-Up Factor. 6 minutes 1) x x ) x 2 – 22x ) x 2 – 12x - 64 Solve each equation. 4) d 2 – 100 = 0 5) z 2 – 2z + 1 = 0 6) t

Transformations Review Vertex form: y = a(x – h) 2 + k The vertex form of a quadratic equation allows you to immediately identify the vertex of a parabola.

5-1 Graphing Quadratic Functions Algebra II CP. Vocabulary Quadratic function Quadratic term Linear term Constant term Parabola Axis of symmetry Vertex.

Warm Up for Lesson 3.5 1)Solve: x 2 – 8x – 20 = 0 2) Sketch the graph of the equation y = 2x – 4.

2-7 Absolute Value Function Objective: I can write and graph an absolute value function.

4.2 Standard Form of a Quadratic Function The standard form of a quadratic function is f(x) = ax² + bx + c, where a ≠ 0. For any quadratic function f(x)

9.1: GRAPHING QUADRATICS ALGEBRA 1. OBJECTIVES I will be able to graph quadratics: Given in Standard Form Given in Vertex Form Given in Intercept Form.

IDENTIFYING CHARACTERISTICS OF QUADRATIC FUNCTIONS A quadratic function is a nonlinear function that can be written in the standard form y = ax 2 + bx.

 I will be able to identify and graph quadratic functions. Algebra 2 Foundations, pg 204.

UNIT 5 REVIEW. “MUST HAVE" NOTES!!!. You can also graph quadratic functions by applying transformations to the parent function f(x) = x 2. Transforming.

Transformations of Functions. The vertex of the parabola is at (h, k).

Bellwork 1.Solve the inequality and Graph the solution 2.Write a standard form of equation of the line desired Through ( 3, 4), perpendicular to y = -

Unit 2 – Quadratic Functions & Equations. A quadratic function can be written in the form f(x) = ax 2 + bx + c where a, b, and c are real numbers and.

Quadratic Functions Unit Objectives: Solve a quadratic equation.

Section 4.1 Notes: Graphing Quadratic Functions

Graphing Linear/Quadratic Equations

Increasing Decreasing Constant Functions.

Do-Now What is the general form of an absolute value function?

2.6 Families of Functions Learning goals

Transformations of Quadratic Functions (9-3)

Investigation Reflection

Find the x and y intercepts.

Inequality Set Notation

Warm-Up 1. On approximately what interval is the function is decreasing. Are there any zeros? If so where? Write the equation of the line through.

Use Absolute Value Functions and Transformations

2.6 Translations and Families of Functions

4.1 Quadratic Functions and Transformations

Graphs of Quadratic Functions

I can Shift, Reflect, and Stretch Graphs

Translating Parabolas

Objectives Transform quadratic functions.

3.4: Graphs and Transformations

Unit 5a Graphing Quadratics

Lesson 5.3 Transforming Parabolas

Chapter 15 Review Quadratic Functions.

Family of Quadratic Functions

Bahm’s EIGHT Steps to Graphing Quadratic Equations (y = ax2 + bx + c) like a CHAMPION! Find the axis of symmetry (x = -b/2a) Substitute.

Also: Study interval notation

Chapter 15 Review Quadratic Functions.

Unit 6 Graphing Quadratics

Functions and Transformations

The vertex of the parabola is at (h, k).

Translations & Transformations

Absolute Value Equations

Graphing Quadratic Functions

Warm up Write the equation in vertex form of the quadratic equation that has been: 1. shifted right 7 and down reflected across the x-axis and shifted.

Unit 4: Transformations and piecewise functions

Bellwork: 2/8/18 Graph. Identify the vertex, axis of symmetry, domain, and range. 1. y = -3x y =(x-1)2 *Have your bellwork for the week out,

Chapter 2 Functions, Equations, and Graphs

Unit 3 Graphing Quadratics

Unit 5 Graphing Quadratics

Unit 5a Graphing Quadratics

Worksheet Key 1) (–∞, –4] 2) [–1, ∞) 3) (–4, ∞) 4) (–∞, –2) 5)

Quadratic Functions and Equations Lesson 1: Graphing Quadratic Functions.

Presentation transcript:

Inequality Set Notation Objective: Students will be able to convert quadratic equations. NCSS: NC.M2.F-BF.3 Understand the effect of transformations on functions Essential Question: How does adding and subtracting constants to your function effect your graph? Words Inequality Set Notation Interval Notation All real numbers All real numbers less than 4 All real numbers less than or equal to 4 All real numbers greater than - 2 All real numbers greater than or equal to - 2 All real numbers greater than 0 and less than 5 All real numbers greater than or equal to 0 and less than or equal to 5 All real numbers greater than or equal to - 6 and less than 5 All real numbers greater than -6 and less than or equal to 5

Quadratic Transformations 8/29 Objective: Students will be able to convert quadratic equations. NCSS: NC.M2.F-BF.3 Understand the effect of transformations on functions Essential Question: How does adding and subtracting constants to your function effect your graph? Lesson Parent function: f(x) = x2 Domain, Range, Axis of Symmetry Add to the function Subtract from the function f(x) = x2 + 4: f(x) = x2 – 4:

Parent function: f(x) = x2 Domain, Range, Axis of Symmetry Objective: Students will be able to convert quadratic equations. NCSS: NC.M2.F-BF.3 Understand the effect of transformations on functions Essential Question: How does adding and subtracting constants to your function effect your graph? Parent function: f(x) = x2 Domain, Range, Axis of Symmetry Add to the x-value Subtract from the x-value f(x) = (x + 4)2 f(x) = (x – 4)2

Parent function: f(x) = x2 Domain, Range, Axis of Symmetry Objective: Students will be able to convert quadratic equations. NCSS: NC.M2.F-BF.3 Understand the effect of transformations on functions Essential Question: How does adding and subtracting constants to your function effect your graph? Parent function: f(x) = x2 Domain, Range, Axis of Symmetry Multiply 0< x < 1 Multiply > 1 f(x) = x2 : f(x) = 2x2 :

Parent function: f(x) = x2 Domain, Range, Axis of Symmetry Objective: Students will be able to convert quadratic equations. NCSS: NC.M2.F-BF.3 Understand the effect of transformations on functions Essential Question: How does adding and subtracting constants to your function effect your graph? Parent function: f(x) = x2 Domain, Range, Axis of Symmetry Multiply a - 1 Graph: f(x) = 3(x – 2)2 + 1 f(x) = - x2 :

Write the equation using the transformations. Objective: Students will be able to convert quadratic equations. NCSS: NC.M2.F-BF.3 Understand the effect of transformations on functions Essential Question: How does adding and subtracting constants to your function effect your graph? Write the equation using the transformations. Vertex form: f(x) = a(x – h)2 + k, where (h,k) is the vertex. Standard form: f(x) = ax2 + bx + c Ex 1. Use f(x) = x2 as the parent function. Reflection across the x – axis, shifts left 1 unit, translates up 5 units Compression of 2/3, moves down 9 units Reflection across the x – axis and stretch of 4

Write the equation using transformations. Ex 2. Objective: Students will be able to convert quadratic equations. NCSS: NC.M2.F-BF.3 Understand the effect of transformations on functions Essential Question: How does adding and subtracting constants to your function effect your graph? Write the equation using transformations. Ex 2.

Write the equation using transformations. Ex 3. Objective: Students will be able to convert quadratic equations. NCSS: NC.M2.F-BF.3 Understand the effect of transformations on functions Essential Question: How does adding and subtracting constants to your function effect your graph? Write the equation using transformations. Ex 3.