Perform the indicated Operations1. 2. 3.

Warm – up #2

1. = = 2. = = = =

Warm – up #2 Solutions

3.

=

=

=

=

=

Warm – up #2 Solutions∙(2+3 𝑖)(2+3 𝑖)

Homework Log

Wed

11/4

Lesson 4 – 7

Learning Objective: To solve using quadratic equations

Hw: Lesson 4 – 7 WS

11/4/15 Lesson 4 – 7 Quadratic Formula

Algebra II

To solve quadratic equations by using quadratic formula

To find discriminant To understand what discriminant describes

Learning Objective

Quadratic FormulaQuadratic Equation

***Must = 0 before solving!!Solve using Quadratic Formula

DiscriminantDiscriminant – tells the nature of the roots (Part under the radical)Discriminant RootsZero 1 real double rootPositive 2 real rootsNegative 2 imaginary roots

DiscriminantFind the discriminant & determine the nature of the roots.1. a = 2 b = –1 c = –15 = 121

= = 1 + 120

2 Real Roots

DiscriminantFind the discriminant & determine the nature of the roots.2. a = 4 b = –20 c = 25 = 0

= = 400 – 400

1 Real Double Root

DiscriminantFind the discriminant & determine the nature of the roots.3. a = 1 b = 4 c = 13 = –36

= = 16 – 52

2 Imaginary Roots

Solve by Quadratic Formula

4.

Set = 0

a = 9 b = 7 c = –1

x ,

Solve by Quadratic Formula

5.

Distribute & Set = 0

a = 1 b = 2 c = –168

x = 12, –14

Solve by Quadratic Formula

6.

Solve by Quadratic Formula

7.

Discriminant = 0

1 Real Double Root

x = 3 and x = 3 (counts twice!)

Solve by Quadratic Formula

8.

x ,

Solve by Quadratic Formula

9.

x ,

x x

Solve by Quadratic Formula

10.

Solve by Quadratic Formula

11.

Solve by Quadratic Formula

12.

Find discriminantDescribe the types of solutionsSolve using Quadratic Formula

Ticket Out the Door

Assignment:

Lesson 4 – 7 WS