Objectives: Be able to graph a quadratic function in vertex form Be able to write a quadratic function in vertex form (2 ways)

Slides:

Advertisements

Similar presentations

6.1/6.2/6.6/6.7 Graphing , Solving, Analyzing Parabolas

Advertisements

EXAMPLE 1 Graph y= ax 2 where a > 1 STEP 1 Make a table of values for y = 3x 2 x– 2– 1012 y12303 Plot the points from the table. STEP 2.

The vertex of the parabola is at (h, k).

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

1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.

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

Quadraticsparabola (u-shaped graph) y = ax2 y = -ax2 Sketching Quadratic Functions A.) Opens up or down: 1.) When "a" is positive, the graph curves upwards.

And the Quadratic Equation……

+ 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.

Warm-Up: you should be able to answer the following without the use of a calculator 2) Graph the following function and state the domain, range and axis.

Graphs of Quadratic Equations. Standard Form: y = ax 2 +bx+ c Shape: Parabola Vertex: high or low point.

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

Goal: Graph quadratic functions in different forms.

10.1 Graphing Quadratic Functions p. 17. Quadratic Functions Definition: a function described by an equation of the form f(x) = ax 2 + bx + c, where a.

Copyright © 2014, 2010, 2006 Pearson Education, Inc. 1 Chapter 3 Quadratic Functions and Equations.

2.2 b Writing equations in vertex form

5.1 Stretching/Reflecting Quadratic Relations

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.

Do Now: Pass out calculators. Work on Practice EOC Week # 12 Write down your assignments for the week for a scholar dollar.

Objectives Vocabulary zero of a function axis of symmetry

5.1 Graphing Quadratic Functions Algebra 2. Learning Check I can graph quadratic equations of the form y = (x – h) 2 + k, and identify the vertex and.

Objective: To us the vertex form of a quadratic equation 5-3 TRANSFORMING PARABOLAS.

Graphing Quadratic Equations

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.

Graphing Quadratic Functions

4-1 Quadratic Functions Unit Objectives: Solve a quadratic equation. Graph/Transform quadratic functions with/without a calculator Identify function.

3.2 Properties of Quadratic Relations

Chapter 4 Quadratics 4.3 Using Technology to Investigate Transformations.

Vertex & axis of Symmetry I can calculate vertex and axis of symmetry from an equation.

GRAPHING QUADRATIC FUNCTIONS

7-3 Graphing quadratic functions

4.1 Graph Quadratic Functions in Standard Form

5-3 Transforming Parabolas (Part 2)

Replacing f(x) with k f(x) and f(k x) Adapted from Walch Education.

 How would you sketch the following graph? ◦ y = 2(x – 3) 2 – 8  You need to perform transformations to the graph of y = x 2  Take it one step at a.

Quadratic Functions Algebra III, Sec. 2.1 Objective You will learn how to sketch and analyze graph of functions.

1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.

Transformations Review Vertex form: y = a(x – h) 2 + k The vertex form of a quadratic equation allows you to immediately identify the vertex of a parabola.

QUADRATIC EQUATIONS in VERTEX FORM y = a(b(x – h)) 2 + k.

5.3 Transformations of Parabolas Goal : Write a quadratic in Vertex Form and use graphing transformations to easily graph a parabola.

Chapter 5.2/Day 3 Solving Quadratic Functions by Graphing Target Goal: 1. Solve quadratic equations by graphing.

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

Ch. 5 Notes Page 31 P31 5.3: Transforming Parabolas “I am only one, but I am one. I cannot do everything, but I can do something. And I will not let what.

Algebra I Algebraic Connections Algebra II Absolute Value Functions and Graphs.

9-3 Graphing y = ax + bx + c 2 1a. y = x - 1 for -3

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

Objective: Students will be able to 1)Find the axis of symmetry 2)Find the vertex 3)Graph a quadratic formula using a table of values.

WARM-UP: Graphing Using a Table x y = 3x  2 y -2 y = 3(-2)  2 -8 y = 3(-1)  y = 3(0)  y = 3(1)  y = 3(2)  2 4 GRAPH. y = 3x 

Algebra 2. Lesson 5-3 Graph y = (x + 1) 2 – Step 1:Graph the vertex (–1, –2). Draw the axis of symmetry x = –1. Step 2:Find another point. When.

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

 I will be able to identify and graph quadratic functions. Algebra 2 Foundations, pg 204.

10-2 Graphing Quadratic Functions. Quadratic Functions (y = ax 2 +bx+c) When a is positive, When a is negative, When c is positive When c is negative.

Key Components for Graphing a Quadratic Function.

Transformations of Functions. The vertex of the parabola is at (h, k).

Section 2.5 Transformations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

5-3 T RANSFORMING PARABOLAS ( PART 1) Big Idea: -Demonstrate and explain what changing a coefficient has on the graph of quadratic functions.

5-3 Using Transformations to Graph Quadratic Functions.

WARM UP 1.Use the graph of to sketch the graph of 2.Use the graph of to sketch the graph of.

Unit 2 – Quadratic Functions & Equations. A quadratic function can be written in the form f(x) = ax 2 + bx + c where a, b, and c are real numbers and.

4.1 Quadratic Functions and Transformations

Translating Parabolas

parabola up down vertex Graph Quadratic Equations axis of symmetry

Lesson 5.3 Transforming Parabolas

Find the x-coordinate of the vertex

8.4 - Graphing f (x) = a(x − h)2 + k

Lesson 5.3 Transforming Parabolas

2.1 Transformations of Quadratic Functions

The vertex of the parabola is at (h, k).

Presentation transcript:

Objectives: Be able to graph a quadratic function in vertex form Be able to write a quadratic function in vertex form (2 ways)

Vertex Form of a Quadratic Reflection over x-axis if a is negative, vertical stretch (a > 1) or shrink (a < 1) Horizontal translation (opposite of what you see!) *The vertex of the parabola is (h, k) and the axis of symmetry is x = h. Vertex Form of a Quadratic Equation: Vertical Translation

xy a. Vertex (horiz. and vert. translation) b. Axis of symmetry c. Table Point Vertex Corresp. d. Ask: Correct reflection? Correct stretch or shrink? Graphing Equations in Vertex Form

a. Vertex (horiz. and vert. translation) b. Axis of symmetry c. Table Point Vertex Corresp. d. Ask: Correct reflection? Correct stretch or shrink? xy Try this one…

Ex 4) Write the equation for the following parabola in vertex form: y = a(x – h) 2 + k Vertex Form from Graph

Ex 4) Write the equation for the following parabola in vertex form: y = a(x – h) 2 + k Vertex Form from Graph

Ex5) Write y = 2x x + 7 in vertex form. a. Find the x-coordinate of the vertex (h): b. Find the y-coordinate of the vertex (k): c. Substitute a, h, and k into vertex form: Vertex Form from Standard Form

Ex5) Write y = –7x 2 – 70x – 169 in vertex form. a. Find the x-coordinate of the vertex (h): b. Find the y-coordinate of the vertex (k): c. Substitute a, h, and k into vertex form: Vertex Form from Standard Form