Quadratic Functions Section 2.2. Objectives Rewrite a quadratic function in vertex form using completing the square. Find the vertex of a quadratic function.

Slides:

Advertisements

Similar presentations

1.4 – Shifting, Reflecting, and Stretching Graphs

Advertisements

Quadratic Functions.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Sullivan Algebra and Trigonometry: Section 4.3 Quadratic Functions/Models Objectives Graph a Quadratic Function Using Transformations Identify the Vertex.

Section 3.6 Quadratic Equations Objectives

The Graph of a Quadratic Function

Math 426 FUNCTIONS QUADRATIC.

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?

Quadratic Functions, Quadratic Expressions, Quadratic Equations

12-4 Quadratic Functions CA Standards 21.0 and 22.0 CA Standards 21.0 and 22.0 Graph quadratic functions; know that their roots are the x-intercepts; use.

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.

4.10: Write Quadratic Functions and Models HW: p.312 – 313 (4, 12, 18, 22, 28, 34) Test : Wednesday.

Solving Quadratic Equations by Graphing

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 4.3 Quadratic Functions and Their Properties.

1.4 More Quadratic Functions and Applications 1 In the previous section, we transformed a quadratic function from the form f(x)=ax 2 +bx+c to the form.

Write a quadratic function in vertex form

Chapter 2 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Quadratic Functions.

Chapter 2 Polynomial and Rational Functions 2.1 Quadratic Functions Definition of a polynomial function Let n be a nonnegative integer so n={0,1,2,3…}

Graphing Quadratic Functions and Transformations.

Solving Quadratic Equation by Graphing

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.

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.

Quadratic Functions and Their Graphs More in Sec. 2.1b.

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

Quadratic Functions & Models How Gravity Has Made the Parabola an Important Graph.

EXAMPLE 1 Write a quadratic function in vertex form Write a quadratic function for the parabola shown. SOLUTION Use vertex form because the vertex is given.

Quadratic Functions and Their Graphs

9.4 Graphing Quadratics Three Forms

Section 3.1 Quadratic Functions; Parabolas Copyright ©2013 Pearson Education, Inc.

Quadratic Functions & Models MATH Precalculus S. Rook.

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.

Graphing Quadratic Equations Standard Form & Vertex Form.

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.

Sullivan Algebra and Trigonometry: Section 4.1 Objectives Graph a Quadratic Function Using Transformations Identify the Vertex and Axis of Symmetry of.

Solving Quadratic Equations

 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:

 Objectives: Solve quadratic equations that cannot be factored by completing the square  Vocabulary: Perfect Square Trinomial- A trinomial 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.

Section 5-4(e) Solving quadratic equations by factoring and graphing.

Section 3.1 Review General Form: f(x) = ax 2 + bx + c How the numbers work: Using the General.

Working With Quadratics M 110 Modeling with Elementary Functions Section 2.1 Quadratic Functions V. J. Motto.

Jeff Bivin -- LZHS Quadratic Equations. Jeff Bivin -- LZHS Convert to Standard Form f(x) = 5x x + 46 f(x) = 5(x 2 - 8x + (-4) 2 ) f(x)

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.

Algebra II Chapter 2 Study Team Strategy Hot Seat Objective: Prepare for the Chapter 2 TAPS tomorrow & Individual Test Wednesday

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

5-1 Graphing Quadratic Functions Algebra II CP. Vocabulary Quadratic function Quadratic term Linear term Constant term Parabola Axis of symmetry Vertex.

F(x) = x 2 Let’s review the basic graph of f(x) = x xf(x) = x

Interpreting Various Forms of Quadratic Equations (2.1.2) October 2nd, 2015.

Section 3.1 Day 2 – Quadratic Functions After this section you should be able to: Graph a quadratic function with and without a calculator. Find the coordinates.

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.

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.

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

Quadratics Review – Intercept & Standard Form August 30, 2016.

Quadratic Functions PreCalculus 3-3. The graph of any quadratic function is called a parabola. Parabolas are shaped like cups, as shown in the graph below.

Write a quadratic function in vertex form

Solving Quadratic Equations by the Complete the Square Method

Graphing Quadratics in Standard Form

Quadratics Review – Intercept & Standard Form

Review: Simplify.

MATH 1310 Section 3.5.

Welcome Activity Pass out the WKS on:

MATH 1310 Section 3.5.

Warm up Graph 1. y = 3x² - 6x y = -x² + 2x – 1

Algebra 1 Warm Ups 12/11.

Presentation transcript:

Quadratic Functions Section 2.2

Objectives Rewrite a quadratic function in vertex form using completing the square. Find the vertex of a quadratic function. Find x-intercepts and y-intercepts of a quadratic function. Write a quadratic function given two points.

Objectives Solve a word problem involving a quadratic function. Determine how a function has been transformed given an equation or a graph. Given a description of a transformed function, write the equation of the new function.

Vocabulary quadratic function parabola standard form of a quadratic equation completing the square

Given the function below find the vertex, x-intercepts, and y-intercepts:

Find a function whose graph is a parabola with vertex (-2, -9) and that passes through the point (-1, -6).

The profit function for a computer company is given by where x is the number of units produced (in thousands) and the profit is in thousand of dollars.

Determine how many (thousands of) units must be produced to yield maximum profit.

Determine the maximum profit.

Determine how many units should be produced for a profit of at least 40 thousand dollars.

The graph of the function can be obtained from the graph of f(x) by what transformation?

Given after performing the following transformations, write the equation of the new transformed function: reflect over the x-axis shift upward 48 units shift 85 units to the right