Unit #3: Quadratics 5-3: Translating Parabolas

Slides:

Advertisements

Similar presentations

Essential Question(s): How can you tell if a quadratic function a) opens up or down b) has a minimum or maximum, and c) how many x-intercepts it has?

Advertisements

The equation for a parabola can come in 2 forms: General formf(x) = ax 2 + bx + c Standard formf(x) = a(x – h) 2 + k Each form has its advantages. General.

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?

Module 3 Lesson 5: Basic Quadratic Equation Standard Form and Vertex Form Translations Affect of changing a Translations Affect of changing h Translations.

Section 7.5 – Graphing Quadratic Functions Using Properties.

How do I write quadratic functions and models? 7.2 Write Quadratic Functions and Models Example 1 Write a quadratic function in vertex form Write a quadratic.

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.

MTH 065 Elementary Algebra II Chapter 11 Quadratic Functions and Equations Section 11.7 More About Graphing Quadratic Functions.

13.2 Solving Quadratic Equations by Graphing CORD Math Mrs. Spitz Spring 2007.

Chapter 16 Quadratic Equations.

Essential Question: How do you determine whether a quadratic function has a maximum or minimum and how do you find it?

+ 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.

Quadratic Functions. The graph of any quadratic function is called a parabola. Parabolas are shaped like cups, as shown in the graph below. If the coefficient.

WARM UP WHAT TO EXPECT FOR THE REST OF THE YEAR 4 May The Discriminant May 29 Chapter Review May 30 Review May 31 Chapter 9 Test June Adding.

Copyright © 2011 Pearson Education, Inc. Quadratic Functions and Inequalities Section 3.1 Polynomial and Rational Functions.

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

Quadratic Functions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph.

Polynomial Function A polynomial function of degree n, where n is a nonnegative integer, is a function defined by an expression of the form where.

Lesson 9-2 Graphing y = ax + bx + c Objective: To graph equations of the form f(x) = ax + bx + c and interpret these graphs. 2 2.

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.7 – Analyzing Graphs of Quadratic.

Fireworks – Finding Intercepts

9.4 Graphing Quadratics Three Forms

REVIEW FOR QUIZ ALGEBRA 1 CP MS. BATTAGLIA & MR. BALDINO.

Factor and Solve: 1.x² - 6x – 27 = 0 2.4x² - 1 = 0 Convert to Vertex Format by Completing the Square (hint: kids at the store) 3. Y = 3x² - 12x + 20.

Fireworks – From Standard to Vertex Form

 What are the three forms a quadratic equation can be written in? Vertex Standard Factored.

Graphing Quadratic Equations Standard Form & Vertex Form.

Today in Pre-Calculus Go over homework Notes: –Quadratic Functions Homework.

Learning Task/Big Idea: Students will learn how to find roots(x-intercepts) of a quadratic function and use the roots to graph the parabola.

Graphing Quadratic Equations

Graphing Quadratic Functions

Solving Quadratic Equations

6-6 Analyzing Graphs of Quadratic Functions Objective.

2.3 Quadratic Functions. A quadratic function is a function of the form:

Summary of 2.1 y = -x2 graph of y = x2 is reflected in the x- axis

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

Chapter 9.1 Notes. Quadratic Function – An equation of the form ax 2 + bx + c, where a is not equal to 0. Parabola – The graph of a quadratic function.

Fireworks – Vertex Form of a Quadratic Equation

WARM UP WHAT TO EXPECT FOR THE REST OF THE YEAR 4 May The Discriminant May 29 Chapter Review May 30 Review May 31 Chapter 9 Test June Adding.

Friday, March 21, 2013 Do Now: factor each polynomial 1)2)3)

Graphs of Quadratic Functions Graph the function. Compare the graph with the graph of Example 1.

Graphing & Solving Quadratic Inequalities 5.7 What is different in the graphing process of an equality and an inequality? How can you check the x-intercepts.

3.2-1 Vertex Form of Quadratics. Recall… A quadratic equation is an equation/function of the form f(x) = ax 2 + bx + c.

Warm Up Expand the following pairs of binomials: 1.(x-4)(2x+3) 2.(3x-1)(x-11) 3.(x+8)(x-8)

Section 3.3 Quadratic Functions. A quadratic function is a function of the form: where a, b, and c are real numbers and a 0. The domain of a quadratic.

 What are the three forms a quadratic equation can be written in? Vertex Standard Factored.

Warm Up for Lesson 3.6 Identify the vertex of each parabola: (1). y = -(x + 3) 2 – 5 (2). y = 2x (3). y = 3(x – 1) (4). y = -5(x + 4) 2 (5).

Warm Up Important Properties: 1.The graph will open up if ‘a’ ___ 0 and down if ‘a’ ___ 0 3.The vertex formula for: vertex format is: standard format is:

Section 8.7 More About Quadratic Function Graphs  Completing the Square  Finding Intercepts 8.71.

Precalculus Section 1.7 Define and graph quadratic functions

Chapter 4 Quadratics 4.2 Vertex Form of the Equation.

Warm Up  1.) What is the vertex of the graph with the equation y = 3(x – 4) 2 + 5?  2.) What are the x-intercepts of the graph with the equation y= -2(x.

Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC.

Quadratic Functions Sections Quadratic Functions: 8.1 A quadratic function is a function that can be written in standard form: y = ax 2 + bx.

GRAPH QUADRATIC FUNCTIONS. FIND AND INTERPRET THE MAXIMUM AND MINIMUM VALUES OF A QUADRATIC FUNCTION. 5.1 Graphing Quadratic Functions.

10.3 Solving Quadratic Equations – Solving Quadratic Eq. Goals / “I can…”  Solve quadratic equations by graphing  Solve quadratic equations using.

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.

Identifying Quadratic Functions. The function y = x 2 is shown in the graph. Notice that the graph is not linear. This function is a quadratic function.

F(x) = a(x - p) 2 + q 4.4B Chapter 4 Quadratic Functions.

7.3 Solving Equations Using Quadratic Techniques

Algebra I Section 9.3 Graph Quadratic Functions

Objectives Identify quadratic functions and determine whether they have a minimum or maximum. Graph a quadratic function and give its domain and range.

Warm-up: Find the equation of the parabola y = ax2 + bx + c that passes through the given points: (-1, 4), (1, -6), (2, -5) CW: 7.1 – 7.3 Systems Quiz.

I will write a quadratic function in vertex form.

5.4 Completing the Square.

Solving Quadratic Equations by Graphing

Objectives Identify quadratic functions and determine whether they have a minimum or maximum. Graph a quadratic function and give its domain and range.

Daily Check If a quadratic decreases from 2 < x < ∞ and the vertex is at (2, -3), how many x intercepts would the quadratic have? A quadratic has a vertex.

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Presentation transcript:

Unit #3: Quadratics 5-3: Translating Parabolas Essential Question: How is the vertex form used in transforming a quadratic function?

5-3: Translating Parabolas Yesterday, we explored quadratic equations in polynomial form: y = ax2 + bx + c Two other forms which are used are x-intercept (factored) form and vertex (transformation) form. Vertex form of a quadratic function is an equation in the form: y = a(x – h)2 + k Just like in polynomial form: If a is positive, the graph opens up If a is negative, the graph opens down

5-3: Translating Parabolas y = a(x – h)2 + k The vertex is found at (h, k) h: Set what’s inside the parenthesis = 0 and solve for x k: Take the number that’s being added to the end of the function. Example Find the vertex of y = (x + 3)2 – 1 Because a = 1 (nothing in front of the parenthesis): The graph opens up. x + 3 = 0 → subtract 3 on each side → x = -3 h = -3, k = -1 The vertex is at (-3, -1).

5-3: Translating Parabolas Determine the vertex of the quadratic function and whether the graph opens up or down. y = -3(x + 2)2 + 4 Opens: Vertex: y = 2(x – 2.5)2 – 5.5 y = -½(x – 2)2 Down (-2, 4) Up (2.5, -5.5) Down (2, 0)

5-3: Translating Parabolas To find the y-intercept: Simply substitute “0” in for x and simplify Example: y = -2(x – 3)2 + 4 y = -2(0 – 3)2 + 4 = -2(-3) 2 + 4 = -2(9) + 4 = -18 + 4 = -14 The y-intercept is at (0, -14)

5-3: Translating Parabolas To convert into polynomial form: FOIL the parenthesis DISTRIBUTE (if necessary) the number outside COMBINE like terms Example: y = -2(x – 3)2 + 4 y = -2(x – 3)2 + 4 = -2(x – 3)(x – 3) + 4 = -2(x2 – 6x + 9) + 4 = -2x2 + 12x – 18 + 4 y = -2x2 + 12x – 14

5-3: Translating Parabolas Determine the y-intercept of the quadratic function and convert the function into polynomial form. y = -3(x + 2)2 + 4 y-intercept: Polynomial form: y = (x – 3)2 – 4 y = -½(x – 2)2 (0, -8) y = -3x2 – 12x – 8 (0, 5) y = x2 – 6x + 5 (0, -2) y = -½x2 + 2x – 2

5-3: Translating Parabolas Assignment Page 251 Problems 1-11, odd Ignore the directions!!! Tell me: Whether the graph opens up or opens down The vertex The y-intercept The function written in polynomial form Note: You may want to do part (d) before part (c) Tomorrow, Practice with graphing Friday, Quiz on 5-1 through 5-3