Quadratic Functions and Equations

Slides:



Advertisements
Similar presentations
Factor and Solve Quadratic Equations
Advertisements

Quadratic Functions Chapter 7. Vertex Form Vertex (h, k)
Quadratic Functions.
QUADRATIC EQUATIONS AND FUNCTIONS
Algebra 2 Chapter 5 Notes Quadratic Functions.
Quadratic Equations and Quadratic Functions Review.
16 Days. Two Days  Review - Use FOIL and the Distributive Property to multiply polynomials.
Properties of Graphs of Quadratic Functions
Chapter 7 Quadratic Equations and Functions
Algebra 2 Chapter 5 Notes Quadratic Functions.
Algebra I Chapter 8/9 Notes. Section 8-1: Adding and Subtracting Polynomials, Day 1 Polynomial – Binomial – Trinomial – Degree of a monomial – Degree.
Copyright © 2014, 2010, 2006 Pearson Education, Inc. 1 Chapter 3 Quadratic Functions and Equations.
Quadratics Review Day 1. Multiplying Binomials Identify key features of a parabola Describe transformations of quadratic functions Objectives FOILFactored.
Quadratic Formula Sam Scholten. Graphing Standard Form Graphing Standard form: Standard form in Quadratic functions is written as: Y = ax 2 +bx+c. The.
Algebra 2: Unit 5 Continued
Quadratic Functions and Parabolas Present by Michael Ai.
Direction: _____________ Width: ______________ AOS: _________________ Set of corresponding points: _______________ Vertex: _______________ Max or Min?
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.
CHAPTER 4.
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
Chapter 9.  Pg. 546 – 552  Obj: Learn how to graph quadratic functions.  Content Standards: F.IF.7.a, A.CED.2, F.IF.4, F.IF.5, and F.BF.3.
ALGEBRA 2 – CHAPTER 5 QUADRATICS. 5-2 PROPERTIES OF PARABOLAS.
CHAPTER 10 LESSON OBJECTIVES. Objectives 10.1 Students will be able to: Identify quadratic functions and determine whether they have a minimum or maximum.
Solving Quadratics Algebra 2 Chapter 3 Algebra 2 Chapter 3.
Quadratics. Quadratic Equations a quadratic equation is an equation of degree 2, meaning that the highest exponent of this function is 2.
3x²-15x+12=0 1.-Find the GCF 2.-then place two sets of parenthesis 3.-factor the front term 4.-then find two factors of the last term that add up to the.
2.1 Linear and Quadratic Functions and Modeling Objective: Students will be able to identify specific types of functions, describe properties of those.
Section 2.5 – Quadratic Equations
Quadratic Function A quadratic function is defined by a quadratic or second-degree polynomial. Standard Form
Factor each polynomial.
Quadratic Graphs and Their Properties
Graphing Quadratic Functions Solving by: Factoring
Algebra I Chapter 8/9 Notes.
Quadratic Equations P.7.
Chapter 3 Quadratic Functions
Lesson 1-7 `Quadratic Functions and their Graphs Object
Quadratic Functions, Quadratic Expressions, Quadratic Equations
Do-Now What is the general form of an absolute value function?
Introductory Algebra Glossary
Polynomials and Polynomial Functions
Section 5-3: X-intercepts and the Quadratic Formula
Functions, Equations, and Graphs
4.1 Quadratic Functions and Transformations
(Sections 4-5 pt. 1 & 2, 4-6 pt. 1, 4-7, 4-8 pt. 1 & 2)
Quadratic Equations and Quadratic Functions
Translating Parabolas
Copyright © Cengage Learning. All rights reserved.
Solving a Quadratic Equation by Graphing
5.1 Modeling Data with Quadratic Functions
GRAPHING QUADRATIC FUNCTIONS
“Exploring Quadratic Functions”
Copyright © Cengage Learning. All rights reserved.
9 Chapter Notes Algebra 1.
Objectives Solve quadratic equations by graphing or factoring.
Quadratic Functions The graph of a quadratic function is called a parabola. The parent function is given as This is the parent graph of all quadratic functions.
Warm Up Find the x-intercept of each function. 1. f(x) = –3x + 9 3
Algebra 2/Trig Name __________________________
Solving Quadratic Equations
You can find the roots of some quadratic equations by factoring and applying the Zero Product Property. Functions have zeros or x-intercepts. Equations.
Chapter 8 Quadratic Functions.
Some Common Functions and their Graphs – Quadratic Functions
Chapter 8 Quadratic Functions.
Before: March 19, 2018 For each quadratic function, find the axis of symmetry and vertex, and state whether the function opens upward or downward.
Chapter 8 – Quadratic Functions and Equations
Complex Numbers What you’ll learn
Honors Algebra 2 Chapter 1a Review
Translations & Transformations
Algebra 2 – Chapter 6 Review
Parabolas.
QUADRATIC FUNCTION PARABOLA.
Presentation transcript:

Quadratic Functions and Equations Chapter 4 Quadratic Functions and Equations

4.1 Quadratic Functions and Transformations Pg. 194 – 201 Obj: Learn how to identify and graph quadratic functions. F.BF.3, A.CED.1, F.IF.4, F.IF.6

4.1 Quadratic Functions and Transformations Parabola – the graph of a quadratic function Quadratic Function – an equation that has a degree 2 Vertex Form – Axis of Symmetry – a line that divides the parabola into two mirror images – x=h Vertex of the Parabola –the intersection of the parabola and its axis of symmetry – (h,k)

4.1 Quadratic Functions and Transformations Minimum Value – the y-coordinate of the vertex, if a>0 – the parabola opens upward Maximum Value – the y-coordinate of the vertex, if a <0 – the parabola opens downward Parent Quadratic Function -

4.1 Quadratic Functions and Transformations Reflection, Stretch, and Compression Reflection – a and –a Stretch – a>1 Compression – 0<a<1 Translation of the Parabola Horizontal – y=(x-h)² - move |h| units Vertical – y=x²+k – move |k| units Horizontal and Vertical – y=(x-h)²+k – move |h| units and |k| units

4.2 Standard Form of a Quadratic Function Pg. 202 – 208 Obj: Learn how to graph quadratic functions written in standard form. A.CED.2, F.IF.4, F.IF.6, F.IF.8, F.IF.9

4.2 Standard Form of a Quadratic Function

4.2 Standard Form of a Quadratic Function Properties of a Quadratic Function If a>0, the parabola opens upward. If a<0, the parabola opens downward. The axis of symmetry is x=-b/2a Vertex (-b/2a, f(-b/2a)) Y-intercept (0,c)

4.3 Modeling With Quadratic Functions Pg. 209-214 Obj: Learn how to model date with quadratic functions. F.IF.5, F.IF.4

4.4 Factoring Quadratic Expressions Pg. 216-223 Obj: Learn how to find common and binomial factors of quadratic expressions and factor special quadratic expressions. A.SSE.2

4.4 Factoring Quadratic Expressions Factoring – rewriting an expression as a product of its factors Greatest Common Factor (GCF) of an Expression – a common factor of the terms in the expression – the common factor with the greatest coefficient and the greatest exponent

4.4 Factoring Quadratic Expressions Perfect Square Trinomial – a trinomial that is the square of a binomial Difference of Two Squares -

4.5 Quadratic Equations Pg. 226-231 Obj: Learn how to solve quadratic equations by factoring and graphing. A.CED.1, A.APR.3, A.SSE.1.a

4.5 Quadratic Equations Zero of a Function – where the graph of a function intersects the x-axis Zero-Product Property – If ab=0, then a=0 or b=0.

4.6 Completing the Square Pg. 233 – 239 Obj: Learn how to solve equations by completing the square and rewrite functions by completing the square. A.REI.4.b

4.6 Completing the Square Completing the Square

4.6 Completing the Square Solving an Equation by Completing the Square Rewrite the equation in the form x²+bx=c Complete the square by adding (b/2)² to each side of the equation. Factor the trinomial Find square roots Solve for x

4.7 The Quadratic Formula Pg. 240-247 Obj: Learn how to solve quadratic equations using the Quadratic Formula and determine the number of solutions by using the discriminant. A.REI.4.b

4.7 The Quadratic Formula The Quadratic Formula

4.7 The Quadratic Formula Discriminant b²-4ac Positive – two solutions Zero – one real solution Negative – no real solution

4.8 Complex Numbers Pg. 248 – 255 Obj: Learn how to identify, graph, and perform operations with complex numbers. Learn how to find complex number solutions of quadratic equations. N.CN.1, N.CN.2, N.CN.7, N.CN.8

4.8 Complex Numbers Imaginary Unit – i the complex number whose square is -1 Imaginary Number – any number of the form a + bi Complex Number – a + bi, where a and b are real numbers Pure Imaginary Number – bi Complex Number Plane – real axis and imaginary axis

4.8 Complex Numbers Absolute Value of a Complex Number – its distance from the origin in the complex plane Complex Conjugates a + bi a - bi

4.9 Quadratic Systems Pg. 258 – 264 Obj: Learn how to solve and graph systems of linear and quadratic equations. A.CED.3, A.REI.7, A.REI.11

4.9 Quadratic Systems Solutions of a Linear-Quadratic System Two Solutions One Solution No Solution