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

Slides:



Advertisements
Similar presentations
5-3 Transforming parabolas
Advertisements

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?
Quadratic Functions.
Quadratic Functions and Their Properties
Quadratic Functions, Quadratic Expressions, Quadratic Equations
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.
Solving Quadratic Equations by Graphing
Solve Using Best Method
Solving Quadratic Equation by Graphing
Sec 5.6 Quadratic Formula & Discriminant Quadratic Formula (Yes, it’s the one with the song!) If ax 2 + bx + c = 0 and a ≠ 0, then the solutions (roots)
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.
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?
9.4 Graphing Quadratics Three Forms
JEOPARDY! Graphing Quadratics Graphing Solving using Square Roots Discriminants GO TO FINAL.
Warmup 9-11 Solve the following equations by factoring. Show work! 1.x x - 80 = 0 2.Solve by using the quadratic formula: 4x 2 - 5x - 2 = 0 3.Solve.
Objective - To use the discriminant to determine the number of real solutions for a quadratic. Quadratic FormulaDiscriminant Used to find the roots of.
CA STANDARDS 20.0: Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. Agenda 1.) Lesson.
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.
1 Warm-up Factor the following x 3 – 3x 2 – 28x 3x 2 – x – 4 16x 4 – 9y 2 x 3 + x 2 – 9x - 9.
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.
Graphing Quadratic Equations Standard Form & Vertex Form.
Solving Quadratic Equations by Graphing Quadratic Equation y = ax 2 + bx + c ax 2 is the quadratic term. bx is the linear term. c is the constant term.
Graphing Quadratic Equations
Solving Quadratic Equations
Section 2.4 Analyzing Graphs of Quadratic Functions.
 Graph is a parabola.  Either has a minimum or maximum point.  That point is called a vertex.  Use transformations of previous section on x 2 and -x.
2.3 Quadratic Functions. A quadratic function is a function of the form:
Characteristics of Quadratics
 Objectives: Solve quadratic equations that cannot be factored by completing the square  Vocabulary: Perfect Square Trinomial- A trinomial of the form.
Vertex & axis of Symmetry I can calculate vertex and axis of symmetry from an equation.
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.
Section 4.7 – The Quadratic Formula Students will be able to: To solve equations using the Quadratic Formula To determine the number of solutions by using.
The Quadratic Formula & Discriminant Essential question – How do you solve a quadratic equation using the Quadratic Formula?
Roots, Zeroes, and Solutions For Quadratics Day 2.
Chapter 6-1 Graphing Quadratic Functions. Which of the following are quadratic functions?
Graphs of Quadratic Functions Graph the function. Compare the graph with the graph of Example 1.
$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.
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.
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.
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:
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.
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.
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:
How does the value of a affect the graphs?
Solving Quadratic Equation by Graphing Students will be able to graph quadratic functions.
Graphing Quadratic Functions. The graph of any Quadratic Function is a Parabola To graph a quadratic Function always find the following: y-intercept.
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.
Quadratic Functions Sections Quadratic Functions: 8.1 A quadratic function is a function that can be written in standard form: y = ax 2 + bx.
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.
10.3 Solving Quadratic Equations – Solving Quadratic Eq. Goals / “I can…”  Solve quadratic equations by graphing  Solve quadratic equations using.
SOLVE QUADRATIC EQUATIONS BY USING THE QUADRATIC FORMULA. USE THE DISCRIMINANT TO DETERMINE THE NUMBER AND TYPE OF ROOTS OF A QUADRATIC EQUATION. 5.6 The.
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.
Solving Quadratic Equations by Graphing Need Graph Paper!!! Objective: 1)To write functions in quadratic form 2)To graph quadratic functions 3)To solve.
5-2 Properties of Parabolas
Quadratic Functions, Quadratic Expressions, Quadratic Equations
Y Label each of the components of the parabola A: ________________ B: ________________ C: ________________ C B B 1 2.
Solving a Quadratic Equation by Graphing
Quadratic Functions.
E) Quadratic Formula & Discriminant
What are the equations of the following lines?
The Discriminant CA 22.0, 23.0.
Some Common Functions and their Graphs – Quadratic Functions
QUADRATIC FUNCTION PARABOLA.
Presentation transcript:

Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC FUNCTIONS/PARABOLAS #1 Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph

Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC FUNCTIONS/PARABOLAS #2 Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph

Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC FUNCTIONS/PARABOLAS #3 Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph

Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC FUNCTIONS/PARABOLAS #4 Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph

Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC FUNCTIONS/PARABOLAS #5 Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph

Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC FUNCTIONS/PARABOLAS #6 Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph

Standard Form y=ax 2 + bx + c Factor (Factor out the negative first, then factor what is in the parenthesis. Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC FUNCTIONS/PARABOLAS #7 Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph

Standard Form y=ax 2 + bx + c Factor (Factor out the negative first, then factor what is in the parenthesis. Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC FUNCTIONS/PARABOLAS #8 Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph

Standard Form y=ax 2 + bx + c Factor (Factor out the negative first, then factor what is in the parenthesis. Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC FUNCTIONS/PARABOLAS #9 Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph

Standard Form y=ax 2 + bx + c Factor (Factor out the negative first, then factor what is in the parenthesis. Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date 1/14/2009 QUIZ – Quadratic Functions/Parabola Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph

Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date 1/16/2009 Quadratic Functions with Imaginary Roots A Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph

Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date 1/16/2009 Quadratic Functions with Imaginary Roots B Y-intercept a =b =c= Vertex ( x, f (x) ) Axis of Symmetry X-intercepts (show work) Discriminant and # of Solutions Quadratic Formula Graph