Vertex Form of Quadratics

Slides:

Advertisements

Similar presentations

Even & Odd Functions Depending on a functions symmetry, it may be classified as even, or as odd. Depending on a functions symmetry, it may be classified.

Advertisements

6.6 Analyzing Graphs of Quadratic Functions

2.5 Graphing Quadratic Functions. There are two main methods for graphing a quadratic I. From Standard Form f (x) = ax 2 + bx + c Axis of Symmetry: Vertex:

Topic: U2 L1 Parts of a Quadratic Function & Graphing Quadratics y = ax 2 + bx + c EQ: Can I identify the vertex, axis of symmetry, x- and y-intercepts,

Unit 1 – Conic Sections Section 1.3 – The Parabola Calculator Required Vertex: (h, k) Opens Left/RightOpens Up/Down Vertex: (h, k) Focus: Directrix: Axis.

Quadratic Functions Section 2.1. Quadratic  A polynomial function of degree “2”  The graph is a parabola  The inverse of a quadratic DNE because it.

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.

Consider the function: f(x) = 2|x – 2| Does the graph of the function open up or down? 2. Is the graph of the function wider, narrower, or the same.

6-6 Analyzing Graphs of Quadratic Functions Objective.

GRAPHING QUADRATIC FUNCTIONS

Graphing quadratic functions (Section 5.1. Forms of the quadratic function  Standard form  Vertex form  Intercept form.

9.1 – Graphing Quadratic Functions. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5.

Pg. 32/71 Homework HWPg. 69 – 71#17, 30 – 32, 69 – 82 Pg. 56#1 – 25 odd #55I would accept: C(t) = (INT(t)) or C(t) = (t) or C(t)

Advanced Algebra Notes Section 4.9: Graphing Quadratic Inequalities A _________________________________ can be written as follows: Remember when graphing.

Graphing Quadratic Functions using Transformational Form The Transformational Form of the Quadratic Equations is:

Topic 5: Modeling with Linear and Quadratics Functions 5.4 Graphing a Quadratic Function.

Section 5-3 Transforming Parabolas. Standard form vs Vertex Form  Standard form is y = ax 2 +bx+c  Vertex form is y = a(x-h) 2 + k.

Parabolas Objective: Understand Properties of Parabolas, Translate Parabolas, and Quadratic Functions.

Section 10.2 – The Parabola Opens Left/Right Opens Up/Down

Section 9.1 Parabolas.

Coefficients a, b, and c are coefficients Examples: Find a, b, and c.

9.3 Graphing Quadratic Functions

y = ax2 + bx + c Quadratic Function Quadratic Term Linear Term

Quadratic Functions and Their Properties

Graph & find x-intercepts. Verify the solutions by factoring.

Systems of Equations Lesson 41: Solve by using a matrix

Warm Up 1. Graph y = x2 + 4x Identify the vertex and zeros of the function above. vertex:(–2 , –1); zeros:–3, –1.

February 15, 2012 At the end of today, you will be able to use vertex form to find the vertex. Warm-up: Solve: 4x2 – 12x – 63 = 0 Solve by graphing:

Graphing Quadratic Functions

Use Absolute Value Functions and Transformations

parabola up down vertex Graph Quadratic Equations axis of symmetry

Unit 5a Graphing Quadratics

Lesson 5.3 Transforming Parabolas

Lesson 5.4 Vertex Form.

Warm up 1) Graph.

Vertex Form of Quadratics

CHAPTER 6 SECTION 1 GRAPHING QUADRATIC FUNCTIONS

Pick up and do the Bellwork Quiz 9-2. (1-6) Only

ALGEBRA I - SECTION 9-2 (Quadratic Functions)

Graph and Solve Quadratic Inequalities

Find the x-coordinate of the vertex

Graphing Quadratic Functions

Graph Quadratic Equations in Standard form

Unit 6 Graphing Quadratics

Graphing Quadratic Functions

Conics: The Parabola Objectives:

Graphing Quadratic Functions

6.6 Analyzing Graphs of Quadratic Functions

Day 127 – Graphing Quadratics

GRAPHING PARABOLAS To graph a parabola you need : a) the vertex

Questions over tests?.

Lesson 5.3 Transforming Parabolas

Before: March 16, y = x² + 4x y = 3x² + 2

Quadratic Functions.

Graphing Quadratic Functions in Vertex form

Using the AOS and Vertex

4.1 Notes – Graph Quadratic Functions in Standard Form

Graphing Key Equations

Vertex Form of Quadratics

Solving Quadratic Equations by Finding Square Roots

Quadratics 2 Write Equations, Match graphs and equations, describe a graph and identify parts of a graph.

Unit 3 Graphing Quadratics

Unit 5 Graphing Quadratics

y = ax2 + bx + c Quadratic Function

Unit 5a Graphing Quadratics

Presentation transcript:

Vertex Form of Quadratics

We already know: We are learning today:

Why is knowing vertex form important if we already know standard form?? If an equation is in vertex form you should be able to state the axis of symmetry & vertex form with no work.

This is a HIGHLY questioned area of the EOC we will take in may. It will typically appear on the NO CALCULATOR section.

Down 2 (2, 4) Let’s make connections: Graph: Transformations: A is Negative: Upside down 3: Narrower -2 inside: moves right 2 +4 outside: Moves up 4 Down Direction: 2 Axis of Symmetry: (2, 4) Vertex:

Down -5 (-5, 3) Let’s make connections: Graph: Transformations: A is Negative: Upside down 2: Narrower +5 inside: Moves left 5 -3 outside: Moves down 3 Down Direction: -5 Axis of Symmetry: (-5, 3) Vertex:

Down -2 (-2, -1) Let’s make connections: Graph: Transformations: A is Positive: Right side up +2 inside: moves left 2 -1 outside: Moves down 1 Down Direction: -2 Axis of Symmetry: (-2, -1) Vertex:

Let’s make connections: Based off our answer for the last three questions what does each part of vertex form mean? Direction (up or down – positive or negative) a: h: k: Axis of Sym. is OPPOSITE of that number Vertex is (-h, k)

A FUN way to remember what “h” does is…. The HOP-posite! H is the OPPOSITE of the axis of symmetry.

Name the direction, axis of symmetry and vertex of each equation Name the direction, axis of symmetry and vertex of each equation. WITHOUT A CALCULATOR. Direction: Axis of Sym.: Vertex: UP Direction: Axis of Sym.: Vertex: DOWN -1 7 (-1, 4) (7, -2)

Name the direction, axis of symmetry and vertex of each equation Name the direction, axis of symmetry and vertex of each equation. WITHOUT A CALCULATOR. Direction: Axis of Sym.: Vertex: DOWN Direction: Axis of Sym.: Vertex: UP 2 -4 (-4, 1) (2, 0)

Name the direction, axis of symmetry and vertex of each equation Name the direction, axis of symmetry and vertex of each equation. WITHOUT A CALCULATOR. UP Direction: Axis of Sym.: Vertex: UP Direction: Axis of Sym.: Vertex: -8 -4 (-8, -2) (-4, -9)