Objective: To explore the relationship between the graphs of y = f(x) and y = f(x + k), where f(x) is in the form of ax 2 + bx + c. Prepared by Jaco Cheung.

Slides:

Advertisements

Similar presentations

6.1/6.2/6.6/6.7 Graphing , Solving, Analyzing Parabolas

Advertisements

f(x) = x 2 f(x) = 2x 2 Parameter ‘a’ increases from 1 to 2 Parabola stretches vertically.

Quadratic Functions By: Cristina V. & Jasmine V..

School starts at 7:15 for EOCT testing!

4.10: Write Quadratic Functions and Models HW: p.312 – 313 (4, 12, 18, 22, 28, 34) Test : Wednesday.

Quadratic Functions Review / Warm up. f(x) = ax^2 + bx + c. In this form when: a>0 graph opens up a 0 Graph has 2 x-intercepts.

Topic: U2 L1 Parts of a Quadratic Function & Graphing Quadratics y = ax 2 + bx + c EQ: Can I identify the vertex, axis of symmetry, x- and y-intercepts,

Graph of quadratic functions We start with a simple graph of y = x 2. y = x 2 x y Vertex(0, 0) Important features  It is  shaped.  It is symmetrical.

Types of Functions.

10.1 Graphing Quadratic Functions p. 17. Quadratic Functions Definition: a function described by an equation of the form f(x) = ax 2 + bx + c, where a.

Real Zeros of Polynomial Functions

5-1 Modeling Data With Quadratic Functions Big Idea: -Graph quadratic functions and determine maxima, minima, and zeros of function. -Demonstrate and explain.

Algebra 2 Ch.5 Notes Page 30 P Modeling Data with Quadratic Equations.

7-3 Graphing quadratic functions

Solving Quadratic Equations by Graphing!. Quadratic functions vs. Quadratic equations Quadratic fxns are written in the following form f(x) = ax² + bx.

2.7 Use Absolute Value Functions

4.6.2 – Graphing Absolute Value Functions

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.

REVIEW FOR QUIZ 3 ALGEBRA II. QUESTION 1 FACTOR THE FOLLOWING QUADRATIC 3N 2 + 7N + 4 Answer: (3n + 4)(n + 1)

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

(2,5) (-4,3) (-7,-7) (1,-3) x y y = mx + b y = ax 2 + bx + c f(x) = sin x g(x) = e x f(x) = ln (x+5)

2.7 – Use of Absolute Value Functions and Transformations.

Mathematical Studies for the IB Diploma © Hodder Education General equation of the sine 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)

Term 1 Week 8 Warm Ups. Warm Up 9/28/15 1.Graph the function and identify the number of zeros: 2x 3 – 5x 2 + 3x – 2 (Hit the y = ) 2.Identify the expressions.

Last Answer LETTER I h(x) = 3x 4 – 8x Last Answer LETTER R Without graphing, solve this polynomial: y = x 3 – 12x x.

Quadratic Inequalities

Family of Functions: A set of functions whose graphs have basic characteristics in common. For example, all linear functions form a family because all.

Algebra Lesson 10-2: Graph y = ax2 + bx + c

Chapter 4: Quadratic Functions and Equations

Use a graphing calculator to graph the following functions

Lesson: Extension Cubic Functions and Equations

Absolute Value Transformations

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

Objective: Graphs of sine and cosine functions with translations.

Section 5.1 Vertical and Horizontal Shifts

Math NS FUNCTIONS QUADRATIC.

5.6 – The Quadratic Formula And Ch 5 Review

3.1 Quadratic Functions and Models

Graphing Exponential Functions Exponential Growth p 635

The graph of f(x) is depicted on the left. At x=0.5,

Find the x-coordinate of the vertex

Graphical Transformations

Objective Solve quadratic equations by graphing.

Review: Simplify.

Chapter 8 Quadratic Functions.

Some Common Functions and their Graphs – Quadratic Functions

Chapter 10 Final Exam Review

Chapter 8 Quadratic Functions.

3.1 Quadratic Functions and Models

(4)² 16 3(5) – 2 = 13 3(4) – (1)² 12 – ● (3) – 2 9 – 2 = 7

Piecewise-Defined Function

Graphing Quadratic Functions

Selected Problems on Limits and Continuity

Replacing f(x) with f(x)+k and f(x+k) (2.6.1)

Drawing Graphs The parabola x Example y

Quadratic Graphs.

I can graph a function with a table

Exponential Functions

Graphing Quadratic Functions

LINEAR & QUADRATIC GRAPHS

Sec 4.3: HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH

Exponential Functions and Their Graphs

Do Now 3/18/19.

3.2 The Remainder Theorem.

Honors Algebra 2 Chapter 4

Quadratic Functions and Equations Lesson 1: Graphing Quadratic Functions.

Presentation transcript:

Objective: To explore the relationship between the graphs of y = f(x) and y = f(x + k), where f(x) is in the form of ax 2 + bx + c. Prepared by Jaco Cheung & Karen Lee

Questions to think: (1) Are the shapes of the graphs of y = f(x) and y = f(x + k) the same? (2) How can the graph of y = f(x + k) be obtained by translating the graph of y = f(x)?

0 4 c = b = – a = k = y = f(x) = ax 2 + bx + c Select values of a, b & c for the graph of y = f(x)

0 4 c = b = – a = k = Select value of k for the new graph of y = f(x + k) y = f(x) = ax 2 + bx + c y = f(x + k)

0 4 c = b = – a = k = Select another value of k for the new graph of y = f(x + k) y = f(x + k) y = f(x) = ax 2 + bx + c