quadratic functions and equations ch. 4.6 completing the square eq: how can you solve a quadratic...

18

QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

Upload: kathlyn-lambert

Post on 17-Jan-2016

221 views

Category:

Documents

2 download

Report

Download

Tags:

Embed Size (px):

TRANSCRIPT

Page 1: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

QUADRATIC FUNCTIONS AND

EQUATIONS

Ch. 4.6Completing the Square

Page 2: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

BELL WORK

Preview Ch. 4.6 by reading over 232-235.

Describe what you think it means to “complete the square”.

Page 3: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

REVIEW

1. Identify the min/max, and domain/range of the function. Y = 3(x + 3)2 – 4

2. Solve by graphing. X2 + 2x – 6 = 0

Page 4: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

COMPLETING THE SQUARE, BUT FIRST… What is an imaginary number?

An imaginary number is a number whose square is negative

What is a real number?

Informally defining, a real number is a number whose square is non-negative.

Page 5: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

REVIEW- PERFECT SQUARE TRINOMIAL

4x2 + 16x + 16 = 0

Page 6: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

SOLVING BY FINDING SQUARE ROOTS

Page 7: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

SOLVING BY FINDING SQUARE ROOTS

Page 8: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

SOLVING BY FINDING SQUARE ROOTSNow you try…

Page 9: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

SOLVING BY FINDING SQUARE ROOTSNow you try…

Page 10: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

SOLVING A PERFECT SQUARE TRINOMIAL EQUATION

Page 11: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

SOLVING A PERFECT SQUARE TRINOMIAL EQUATION

Page 12: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

COMPLETING THE SQUARE

Page 13: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

COMPLETING THE SQUARENow you try…

Page 14: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

SOLVING BY COMPLETING THE SQUARE

Page 15: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

SOLVE BY COMPLETING THE SQUARE

X2 + 6x - 3 = 0

Page 16: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

SOLVE BY COMPLETING THE SQUARE Now you try…

X2 – 12x + 7 = 0

Page 17: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

SOLVE BY COMPLETING THE SQUARE Now you try…

X2 + 4x + 2 = 0

Page 18: QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.6 Completing the Square EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC

EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY COMPLETING THE SQUARE? I WILL SOLVE QUADRATIC EQUATIONS BY COMPLETING THE SQUARE.

CLOSURE

(On your bell sheet)

Explain the process of completing the square.

Splash Screen. Then/Now You solved quadratic equations by completing the square. Solve quadratic equations by using the Quadratic Formula. Use the discriminant

THIS IS 100 200 300 400 500 Graphing Square roots Completing the Square # of roots Quadratic Formula Solve by Graphing

Lesson 9.6 Solve Quadratic Equations by the Quadratic Formula Essential Question: How do you solve quadratic equations by using the quadratic formula?

Completing square of a quadratic function

California Standards 14.0 Students solve a quadratic equation by factoring or completing the square

Instructions for Use - MATH WITH ERXLEBEN · Instructions for Use ... solve quadratic equations by completing the square and then solve a logic puzzle to unlock the ... Solving Quadratics

Solve each quadratic equation by completing the square. In

REASONING WITH EQUATIONS AND INEQUALITIES - 8% · Web viewStudents will be asked to solve quadratic equations by factoring, completing the square, using square roots, using the quadratic

Sec 1.8 –Revisiting Quadratics Quadratic Formula with ... 1.8 –Revisiting Quadratics Quadratic Formula with Imaginary Solutions Name: Solve the following by completing the square

Chapter 2 2-4 completing the square. objectives *Solve quadratic equations by using the square property * Solve quadratic equations by completing

Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Solve quadratic inequalities by using tables and graphs. Solve quadratic inequalities by using

pnhs.psd202.orgpnhs.psd202.org/documents/TAcosta/1508680165.pdfSolve quadratic equations by taking square roots. Solve quadratic equations ax2 + bx+ c = 0 by completing the square

Aim: Quadratic Formula Course: Adv. Alg. & Trig. Aim: What is the quadratic formula and how do we use it? Do Now: Solve by completing the square: x 2

Lesson 10.3-Solving Quadratic Equations by Completing the Square, pg. 539 Objective: To solve quadratic equations by completing the square.To solve quadratic

Warm-up 1. Solve the following quadratic equation by Completing the Square: x 2 - 10x + 15 = 0 2. Convert the following quadratic equation to vertex format

What is the quadratic formula? Do Now: Solve by completing the square x 2 +8x+15=0 I know the quadratic formula, do you?

3 Quadratic Equations and Complex Numbers · Solve quadratic equations by graphing. Solve quadratic equations algebraically. Solve real-life problems. Solving Quadratic Equations

9.4 Solving Quadratic Equations by Completing the Square · Solve quadratic equations by completing the square. Find and use maximum and minimum values. Solve real-life problems by

1.7 Graphing Quadratic Functions. 1. Find the x-intercept(s). The x-intercepts occur when Solve by: Factoring Completing the Square Quadratic Formula

9.3 Solving Quadratic Equations by Completing the … Chapter 9 Solving Quadratic Equations Solving Quadratic Equations by Completing the Square 9.3 How can you use “completing the

Aim: Completing the Square Course: Adv. Alg. & Trig Aim: How do we solve quadratic equations by completing the square? An archer shoots an arrow into

QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.5 Quadratic Equations EQ: HOW CAN YOU SOLVE A QUADRATIC EQUATION BY FACTORING? I WILL SOLVE A QUADRATIC EQUATION

Chapter 7 Quadratic Equations and Functions. Completing the Square TSWBAT solve quadratic equations by completing the square method

3.5 Quadratic Equations OBJ:To solve a quadratic equation by factoring

FACTORING AND SOLVING QUADRATIC LESSON EQUATIONS 11... · Solving quadratic equations by completing the square We can also solve equations of the form ax2 + bx + c = 0 by completing

Completing the Square. The Quadratic Formula and the Discriminant. What you’ll learn To solve quadratic equations by completing the square. To solve quadratic

Factor and Solve Quadratic Equations

Holt McDougal Algebra 2 5-4 Completing the Square Solve quadratic equations by completing the square. Write quadratic equations in vertex form. Objectives

5.4 – Completing the Square Objectives: Use completing the square to solve a quadratic equation. Use the vertex form of a quadratic function to locate

1.5 – Day 1 Equations. 2 Objectives ► Solve Linear Equations ► Solve a Formula for a Given Variable ► Solve Quadratic Equations ► Solve Quadratic-Type

Aim: How do we use completing the square to solve quadratic … · 2014-09-30 · Aim: How do we use completing the square to solve quadratic equations? ll. Solving Quadratic Equations

SAT Problem of the Day. 5.4 Completing the Square 5.4 Completing the Square Objectives: Use completing the square to solve a quadratic equation

Chapter 11 Section 2. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solving Quadratic Equations by Completing the Square Solve quadratic

9-3B Completing the Square Adapted from Math 8H Completing the Square JoAnn Evans (to solve quadratic equations) You will need a calculator for today’s

10.5 Completing the Square. 10.5 – Completing the Square Goals / “I can…” Solve quadratic equations by completing the square