1.a. Identify the vertex. b. Does the function have a minimum or maximum? What is it? c. Find the domain and range. d. What are the solutions? e. What.

Slides:



Advertisements
Similar presentations
5-3 Transforming parabolas
Advertisements

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.
Essential Question: How do you determine whether a quadratic function has a maximum or minimum and how do you find it?
Solve Using Best Method
Name:__________ warm-up 9-5 R Use a table of values to graph y = x 2 + 2x – 1. State the domain and range. What are the coordinates of the vertex of the.
2.11 Warm Up Graph the functions & compare to the parent function, y = x². Find the vertex, axis of symmetry, domain & range. 1. y = x² y = 2x².
1. Determine if f(x) has a minimum or maximum 2. Find the y-intercept of f(x) 3. Find the equation of the axis of symmetry of f(x) 4. Find the vertex of.
Goal: Graph quadratic functions in different forms.
Graphing and Solving. a)What do they look like? b)How can you tell a function is quadratic? c)What are some terms associated with quadratic functions?
2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt Functions Quadratics 1 Quadratics.
9-1 Graphing Quadratic Functions
Warm-Up Find the vertex, the roots or the y- intercept of the following forms: 1. f(x) = (x-4) f(x) = -2(x-3)(x+4) 3. f(x) = x 2 -2x -15 Answers:
JEOPARDY! Graphing Quadratics Graphing Solving using Square Roots Discriminants GO TO FINAL.
Chapter 5 Quadratic Functions Review. Question 1a Identify the vertex, the axis of symmetry, create a table, then graph. y = x² - 8x + 5.
Definitions 4/23/2017 Quadratic Equation in standard form is viewed as, ax2 + bx + c = 0, where a ≠ 0 Parabola is a u-shaped graph.
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.
5.5 – The Quadratic formula Objectives: Use the quadratic formula to find real roots of quadratic equations. Use the roots of a quadratic equation to locate.
Name: Date: Topic: Solving & Graphing Quadratic Functions/Equations Essential Question: How can you solve quadratic equations? Warm-Up : Factor 1. 49p.
Warm Up 1) Find the solution(s): 2)Find the vertex: f(x) = 2x 2 – 8x + 3.
Graphing Quadratic Equations
Solving Quadratic Equations
Properties of Quadratic Functions in Standard Form.
ANSWER 3. Evaluate the expression. Warm Up for Lesson x 2 when x = 4 ANSWER 128 ANSWER –1 2.–4 + x when x = 9 √ Find the (1)Axis of Symmetry, (2)the.
BM 9: Solving Quadratic Equations. What is on the benchmark tomorrow?
$200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400.
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.
QUADRATIC FUNCTIONS IN STANDARD FORM 4.1B. Review  A quadratic function can be written in the form y = ax 2 + bx + c.  The graph is a smooth curve called.
Chapter 2 Quiz Format and Material  14 questions  Material covers 2-1 Using Transformations to Graph Quadratic Functions 2-2 Properties of Quadratic.
Graphs of Quadratics Let’s start by graphing the parent quadratic function y = x 2.
 Standard Form  y = ax 2 + bx + c, where a ≠ 0  Examples › y = 3x 2 › y = x › y = x 2 – x – 2 › y = - x 2 + 2x - 4.
Bonus! TranslationsSolvingFactoring Quadratic Formula.
FACTORING a). FACTORING a) FACTORING a) FACTORING a)
Unit 9 Review Find the equation of the axis of symmetry, along with the coordinates of the vertex of the graph and the y-intercept, for the following equation.
Unit 3-1: Graphing Quadratic Functions Learning Target: I will graph a quadratic equation and label its key features.
Sample Problems for Class Review
9-3 Graphing y = ax + bx + c 2 1a. y = x - 1 for -3
Section 8.7 More About Quadratic Function Graphs  Completing the Square  Finding Intercepts 8.71.
Quadratic Functions Solving by Graphing Quadratic Function Standard Form: f(x) = ax 2 + bx + c.
1.7 Graphing Quadratic Functions. 1. Find the x-intercept(s). The x-intercepts occur when Solve by: Factoring Completing the Square Quadratic Formula.
Graphing quadratic functions part 2. X Y I y = 3x² - 6x + 2 You have to find the vertex before you can graph this function Use the formula -b 2a a = 3.
M2 Unit 1B: Day 7 MM2A4 Students will solve quadratic equations and inequalities in two variables. MM2A4b Find real and complex solutions of equations.
Big Idea: -Graph quadratic functions. -Demonstrate and explain the effect that changing a coefficient has on the graph. 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.
Do Now: Solve the equation in the complex number system.
5-1 Graphing Quadratic Functions Algebra II CP. Vocabulary Quadratic function Quadratic term Linear term Constant term Parabola Axis of symmetry Vertex.
Quadratic Functions. 1. The graph of a quadratic function is given. Choose which function would give you this graph:
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)
Graphing Quadratic Functions. The graph of any Quadratic Function is a Parabola To graph a quadratic Function always find the following: y-intercept.
Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC.
Class Greeting. Chapter 10 Quadratic Equations and Functions Lesson 10-4 Graphing Quadratic Equations.
Key Components for Graphing a Quadratic Function.
GRAPH QUADRATIC FUNCTIONS. FIND AND INTERPRET THE MAXIMUM AND MINIMUM VALUES OF A QUADRATIC FUNCTION. 5.1 Graphing Quadratic Functions.
SAT Problem of the Day. 5.5 The Quadratic Formula 5.5 The Quadratic Formula Objectives: Use the quadratic formula to find real roots of quadratic equations.
5-2 Properties of Parabolas
Warm Up /05/17 1. Evaluate x2 + 5x for x = -4 and x = 3. __; ___
Warm Up /31/17 1. Evaluate x2 + 5x for x = 4 and x = –3. __; ___
Mrs. Rivas Ch 4 Test Review 1.
Solutions, Zeros, and Roots
Y Label each of the components of the parabola A: ________________ B: ________________ C: ________________ C B B 1 2.
Quadratic Functions.
E) Quadratic Formula & Discriminant
What are the equations of the following lines?
Graphing Quadratic Functions
The Discriminant CA 22.0, 23.0.
Welcome: The graph of f(x) = |x – 3| – 6 is given below
Analysis of Absolute Value Functions Date:______________________
Graphing Quadratic Functions
Warm up Graph the Function using a table Use x values -1,0,1,2,3
Quadratic Functions and Their Properties
Quadratic Functions and Equations Lesson 1: Graphing Quadratic Functions.
Presentation transcript:

1.a. Identify the vertex. b. Does the function have a minimum or maximum? What is it? c. Find the domain and range. d. What are the solutions? e. What is the y-intercept?

2. Graph the function and answer the questions below. y = -x 2 + 4x + 2 a)Does it open up or down? b)What is the axis of symmetry? c)What is the vertex? Is it a minimum or maximum point? d)What is the domain and range? e)What are the solutions? f)What is the y-intercept?

3. Tell me about the graph and ID the vertex. a. y=(x-3) 2 +6 b. y=-2(x+6) 2 +1 c. y=.2(x-5) 2

4. Solve a. (x – 10)(2x + 5) = 0 b. x(x + 5) = 0 Factor c. d.

5. Solve a. b. c. 4x 2 – 18 = –9 x 2 + 4x – 5 = 0 –2x 2 = 20x + 50

6. Solve. Give your answer in simplest form. a.x 2 – 195 = 1 b. 4x = 9 c. Solve 0 = –5x Round to the nearest 0.01.

7a. Solve –3x 2 + 5x = 1 by using the Quadratic Formula. 7b. Find the number of solutions of 5x 2 – 10x – 8 = 0 by using the discriminant.

 pp :  1-5, 9-13,  odd  odd, 33, 35  39, 41, 43, 44  45, 47, 51  53, 55, 59, 61  82, 83, 85, 89  p 82: #27  p 109: #9  p 140: #17