PreCalculus. Bell Ringer: pg 129 #46 HW Requests: pg 152 #1-10 a. The average of three numbers is 70. When the smallest of the three numbers is replaced.

Slides:

Advertisements

Similar presentations

1.4 – Shifting, Reflecting, and Stretching Graphs

Advertisements

3.2 Quadratic Functions & Graphs

Date: 9/12/11- Section: 1.1 Linear models Obj.: SWBAT graph functions with square roots and absolute values. Bell Ringer: Quiz Linear Models (15 minutes)

LIAL HORNSBY SCHNEIDER

Quadratic graphs Today we will be able to construct graphs of quadratic equations that model real life problems.

SFM Productions Presents: Another joyous day continuing your Pre-Calculus experience! 2.1Quadratic Functions and Models.

ACTIVITY 27: Quadratic Functions; (Section 3.5, pp ) Maxima and Minima.

3 Polynomial and Rational Functions © 2008 Pearson Addison-Wesley. All rights reserved Sections 3.1–3.2.

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

Algebra 2 Honors Quadratic Functions.

9 week test review problems Problems like 1-11 are definitely on the test 1. Write an equation for the linear function f satisfying the given conditions.

1.8 QUADRATIC FUNCTIONS A function f defined by a quadratic equation of the form y = ax 2 + bx + c or f(x) = ax 2 + bx + c where c  0, is a quadratic.

Quadratic Functions and Their Graphs More in Sec. 2.1b.

Chapter 2 Polynomial and Rational Functions

5.1: Graphing Quadratic Functions

4 minutes Warm-Up Identify each transformation of the parent function f(x) = x2. 1) f(x) = x ) f(x) = (x + 5)2 3) f(x) = 5x2 4) f(x) = -5x2 5)

Copyright © Cengage Learning. All rights reserved. 2 Polynomial and Rational Functions.

Quadratics Review Day 1. Multiplying Binomials Identify key features of a parabola Describe transformations of quadratic functions Objectives FOILFactored.

Do Now Draw a quick sketch of the following polynomials. Name any changes that have occurred.

Pg. 30/42 Homework Pg. 42 #9 – 14, 20 – 36 even, 43, 46, 49, 53 #15D= (-∞, 3)U(3, ∞); R = (-∞,0)U(0, ∞)#17D= (-∞, ∞); R = [0, ∞) #19D= (-∞, 8]; R = [0,

Objective: SWBAT model real world applications using power functions CRS: Functions Evaluate polynomial functions expressed in function values.

Objective: SWBAT graph Rational Functions Bell Ringer: Reading Across the Content (Vocabulary) Section 2.7 and 2.8 Turn in Take Home Test HW Requests:

SECTION 3.4 POLYNOMIAL AND RATIONAL INEQUALITIES POLYNOMIAL AND RATIONAL INEQUALITIES.

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

Notes Over 9.3 Graphs of Quadratic Functions

Date: 9/19/11- Section: 1.2 Functions, Domain and Range Obj.: SWBAT find the range of functions. Bell Ringer: Turn IN Find the domain of the following:

THE SLIDES ARE TIMED! KEEP WORKING! YOUR WORK IS YOUR OWN! Quadratic Systems Activity You completed one in class… complete two more for homework.

2.1 – Quadratic Functions.

SAT Problem of the Day.

Quadratic Functions Algebra III, Sec. 2.1 Objective You will learn how to sketch and analyze graph of functions.

Holt McDougal Algebra Properties of Quadratic Functions in Standard Form Warm Up Give the coordinate of the vertex of each function. 2. f(x) = 2(x.

PreCalculus. Objective: SWBAT solve problems such as projectile motion (free fall) problems using quadratic functions and apply the properties of exponents.

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

Essential Question: How do you sketch graphs and write equations of parabolas? Students will write a summary of the steps they use toe sketch a graph and.

5.3 Transformations of Parabolas Goal : Write a quadratic in Vertex Form and use graphing transformations to easily graph a parabola.

Geometry. Geometry Date: 11/8/2011 Sect. 4.3 pg ID Check Obj.: SWBAT Parking Lot: Lesson 4-1 pg 760 #1-9; pg 155 #35- 37; 182 # 39, HW Requests:

Ch. 5 Notes Page 31 P31 5.3: Transforming Parabolas “I am only one, but I am one. I cannot do everything, but I can do something. And I will not let what.

12/12/11 Chapter 6 Sect. 6.1 Objective: Understand how to write and use properties of Ratios and Proportions. Homework: pg. 286 #28-35 Announcements: Mini.

Objective: SWBAT understand and apply the Fundamental Theorem of Algebra and the Linear Factorization Theorem to find a polynomial given real and complex.

Date: 8/23/11- Section: Prerequisites P.4 pg Objective: SWBAT write the equation of perpendicular and parallel lines in real world applications.

Date: 10/17/11- Section: 1.3 Obj.: SWBAT analyze the behaviors of 12 Basic Functions by finding the domain, range, continuity, increasingness, decreasingness,

Date: 10/31/11- Section: 1.4 Bell Ringer: Using graph paper, graph the line y = x. Plot the following points on your graph. HW Requests: pg 128 #11-14,

Objectives: Be able to graph a quadratic function in vertex form Be able to write a quadratic function in vertex form (2 ways)

Graphing Quadratics. Finding the Vertex We know the line of symmetry always goes through the vertex. Thus, the line of symmetry gives us the x – coordinate.

Precalculus Section 1.7 Define and graph quadratic functions Any function that can be written in the form: y = ax 2 +bx + c is called a quadratic function.

1.A Function and a Point 2.Equation of a line between 2 points 3.A point on the graph of a function 4.Information from a function’s graph 5.Symbols on.

Quiz P (-3 – 4i)(1 + 2i) = ? (2 – 3i) – (-4 – 5i) = ? 3.

Determine if each is a quadratic equation or not.

Quadratic Functions and Their Graphs

Quadratic Functions In Chapter 3, we will discuss polynomial functions

Vertical Height (In Feet)

Chapter 5 – Quadratic Functions

Consider the function f(x)= 2x2 + 8x – 7.

Warm Up HW: Quadratics Review Worksheet

Lesson 5.3 Transforming Parabolas

Lesson 2.1 Quadratic Functions

Polynomial and Rational Functions

Modeling Data With Quadratic Functions

Lesson 5.3 Transforming Parabolas

Chapter 3: Polynomial Functions

Chapter 3: Polynomial Functions

Section 2.1 Quadratic Functions.

THIS IS Precalc Jeopardy. THIS IS Precalc Jeopardy.

Copyright © Cengage Learning. All rights reserved.

Algebra 2 – Chapter 6 Review

Unit 6 Review Day 1 – Day 2 Class Quiz

Section 2.1 Transformations of Quadratic Functions

Graphing Quadratic Functions

Determine if each is a quadratic equation or not.

Presentation transcript:

PreCalculus

Bell Ringer: pg 129 #46 HW Requests: pg 152 #1-10 a. The average of three numbers is 70. When the smallest of the three numbers is replaced by 75, the average is increased by 5. What is the number that was replaced by 75? In class: inherited domains for inverses pg 129 #48. (pg 140 #35- 38, 47-50) Homework : pg 175 # 1-6, 8, 10, 12 Announcements : Binders due 12/2 Date: 11/14/11 Obj: SWBAT algebraically and graphically represent translations, reflections, stretches, and shrinks of functions, understand Inherited domains from inverses and recognize polynomial functions.

Slide 2- 3 Polynomial Function

Objective: SWBAT find the vertex and axis of symmetry and write the equation of quadratic function in standard and vertex form. Bell Ringer: pg 139 #13-16; HW Requests: pg 175 # 1-6, 8, 10, 12 Exit Ticket: (p. 176 # odds). Students will sketch problems 23 and 25. Homework: p. 176 #24-32 evens Parking Lot: a. The average of three numbers is 70. When the smallest of the three numbers is replaced by 75, the average is increased by 5. What is the number that was replaced by 75? Announcements : Binders due 12/2 Date: 11/15/11

Slide 1- 5 Stretches and Shrinks Watch your fractions Horizontal Stretches or Shrinks But c > 0

Characterizing the Nature of a Quadratic Function The y-coordinate, (k),of the vertex is f(h) =h (h,k)

Slide 2- 7 Vertex Form of a Quadratic Equation

Objective: SWBAT find the vertex and axis of symmetry and write the equation of quadratic function in standard and vertex form. Bell Ringer: Correct problems from “Properties of Parabolas” worksheet; HW Requests: pg 176 #24-32 evens Exit Ticket: Complete Properties of Parabolas handout from yesterday Homework: p. 176 #34, 36, Practice – Analyzing Graphs of Quadratic Functions Worksheet 1-15 ; Read pg 172 Free Fall Announcements : Make-up Wednesday Sect Quiz 6 th Per. Asia Clark, D. Lee, J. Reed, D. Weathersby, Chamone Williams Binders due 12/2 Date: 11/16/11

Slide 2- 9 Example Finding the Vertex and Axis of a Quadratic Function 1. Rewrite the equation but use the method of completing the square to find vertex form. 2. Write an equation for the parabola with vertex (1, 3), point (0, 5).

Characterizing the Nature of a Quadratic Function

Graph Vertex Form of a Quadratic Equation

Objective: SWBAT solve problems such as projectile motion (free fall) problems using quadratic functions. Bell Ringer: Go over Exit Ticket HW Requests: 6-6 Practice – Analyzing Graphs of Quadratic Functions Worksheet 1-15 Exit Ticket: Complete yesterday’s Properties of Parabolas handout add #3, 4 (4 min.) In class worksheet Homework: p. 176 #34, 36, 38, Announcements : Make-up Wednesday Sect Quiz 6 th Per. Lee, Weathersby Quiz Tuesday 2.1 Binders due 12/2 Date: 11/17/11

Vertex Form of a Quadratic Equation

Pdemsy 117, 118 Vertical Free-Fall Motion An object is tossed upward with an initial velocity of 15 ft/sec. from a height of 4 ft. What is the object’s maximum height? How long does it take the object to reach its maximum height? A ball is thrown across a field. Its path can be described by the equation y = x 2 +.2x + 5. where x is the horizontal distance (in feet) and y is the height (in feet). What is the ball’s maximum height? How far had it traveled horizontally to reach its maximum height? Max values at the vertex (h,k)