 Factoring (3)  Solving Quadratics (3)  Imaginary Numbers (2)  Extraneous Solutions (1) Functions:  Finding Zeroes (2)  Finding Minimum via TI 84+

Slides:

Advertisements

Similar presentations

solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.

Advertisements

Solving Radical Equations and Inequalities 5-8

Remember! For a square root, the index of the radical is 2.

7.8 Equations Involving Radicals. Solving Equations Involving Radicals :  1. the term with a variable in the radicand on one side of the sign.  2. Raise.

Chapter 2: Equations and Inequalities 2.4: Other Types of Equations

7.3 Solving Radical Equations

A radical equation is an equation that contains a radical.

Lesson 13.4 Solving Radical Equations. Squaring Both Sides of an Equation If a = b, then a 2 = b 2 Squaring both sides of an equation often introduces.

Solve an equation with an extraneous solution

Notes Packet 10: Solving Quadratic Equations by the Quadratic Formula.

Objectives Define and use imaginary and complex numbers.

Solving Quadratic Equations – The Discriminant The Discriminant is the expression found under the radical symbol in the quadratic formula. Discriminant.

Section 6.6: Solve Radical Equations Starter: CC 6.5 Part 2.

Objectives: 1.Be able to solve a radical equation. 2.Be able to solve an equation that contains a rational exponent. Critical Vocabulary: Rational Exponents,

Tonight’s Homework: 6-6: (page 456) (evens): 4 – 18, 24, 28, 32 – 38, 46, 50, 58 (17 points) (17 points)

Solving Equations by Extracting Roots

Chapter 8: Irrational Algebraic Functions

Objectives Define and use imaginary and complex numbers.

Solving Radical Equations Module 14 Topic 4.

Solving equations Section 1.4.

Solve an equation with an extraneous solution

Section 8-1: Introduction to Irrational Algebraic Functions.

Solving Quadratic Equations

Feb 9 and 10 Solving Square Root Equations. A radical equation is an equation that has a variable in a radicand (or a variable with a fractional exponent)

Warm up! Simplify:. Solving Radical Equations What is a radical equation? An equation that contains a radical expression with a variable in the radicand.

Introduction to Quadratic Equations & Solving by Finding Square Roots Chapter 5.3.

Derivation of the Quadratic Formula The following shows how the method of Completing the Square can be used to derive the Quadratic Formula. Start with.

Section 1.6 Other Types of Equations. Polynomial Equations.

Tom Worthing Intermediate Algebra All rights reserved. 1 Higher order equations Use Factoring method or calculator Know how many roots you will have Determine.

Taking the n th Root to Solve Equations Chapter 7.1.

Solving Radical Equations Chapter 7.6. What is a Radical Equation? A Radical Equation is an equation that has a variable in a radicand or has a variable.

Introduction to Complex Numbers Adding, Subtracting, Multiplying Complex Numbers.

Deriving the Quadratic Formula. The Quadratic Formula The solutions of a quadratic equation written in Standard Form, ax 2 + bx + c = 0, can be found.

Warm Up Simplify each expression. Assume all variables are positive

How do I use the imaginary unit i to write complex numbers?

A radical equation is an equation that contains a radical. BACK.

Radical Equation Equation with a variable under radical sign Extraneous Solutions: Extra solutions that do not satisfy original equation because of the.

Warm-Up Find the inverse: 1.3y = 12x f(x) = ½x + 8.

x + 5 = 105x = 10  x = (  x ) 2 = ( 5 ) 2 x = 5 x = 2 x = 25 (5) + 5 = 105(2) = 10  25 = 5 10 = = 10 5 = 5.

11.3 Solving Radical Equations Definitions & Rules Simplifying Radicals Practice Problems.

Algebra 2 Solving Radical Equations Section 7-5 Solving Square Root and Other Radical Equations Lesson 7-5.

SOLVING QUADRATICS: THE SQUARE ROOT PRINCIPLE PART 3.

Section 2.5 – Quadratic Equations

Aim #1.6: How do we solve other types of equations?

Chapter 4 Quadratic Equations

Objectives Solve quadratic equations by factoring.

Solve Radical Equations

Objective Solve radical equations..

Radical Functions and Rational Exponents

Objectives Define and use imaginary and complex numbers.

Let’s Review the Quadratic Formula & Completing the Square!!

Section 1.6 Other Types of Equations

3-8 Solving Radical equations

Warm-up: Solve: 2x2 + 4x – 5 = 0 HW : pg (25, 27, 31, 43, 46, 47, 64, 67, 76, 93, 96, 100, , 107, 108,117, 119)

Solving Radical Equations

1.4 Solving Equations Using a Graphing Utility

Solving Radical Equations

SECTION 10-4 : RADICAL EQUATIONS

2.1 Solving Radical Equations

3.4 – The Quadratic Formula

Solving a Radical Equation

Aim: How do we solve radical equations?

Notes Over Using Radicals

Objective Solve radical equations.. Objective Solve radical equations.

College Algebra 1.6 Other Equations

Lesson 5–5/5–6 Objectives Be able to define and use imaginary and complex numbers Be able to solve quadratic equations with complex roots Be able to solve.

Complete the Square January 16, 2017.

Section 5.8 Solving Radical Equations

Equations Involving Absolute Value

Section 1.6 Other Types of Equations

Presentation transcript:

 Factoring (3)  Solving Quadratics (3)  Imaginary Numbers (2)  Extraneous Solutions (1) Functions:  Finding Zeroes (2)  Finding Minimum via TI 84+  Add/Subt/Mult/Div functions: f(x) and g(x)  Simplifying Expressions w/ Exponents (4)  Solving Equations w/Radicals - Irrational Expressions (2)  Solving Given the value of independent variable

Significance of Signs within a Quadratic Factoring  44-22x  13y y  x 2 -8x-33  x 2 +13x-14 Solving Quadratics  x 2 -2x-35 = 0  x 3 -4x 2 +3x = 0  3 x 2 +27x+60 = 0

Extraneous Solutions - When do they occur? :   Imaginary #s: Divide Exponent by 4 and look at Remainder i 1 = √–1 i 2 = – 1 i 3 = – 1 √–1 i 4 = + 1 Simplify Expressions with Exponents For example: i 6 = – 1

Imaginary #s: Divide Exponent by 4 and look at Remainder i 1 = √–1 i 2 = – 1 i 3 = – 1 √–1 i 4 = i 0 = + 1 Simplify Expressions with Exponents i 2 i 22 i 300 ( √–15 ) ( √–1 )

 f(x) = 2x-32  f(x) = x 2 +7x  f(x) = x 2 +7x-8  f(x)= x 2 +9x  Composition  f(x) = –2x 2 +3, g(x)= 3, h(x)=x-4  What is f(g(x)) = ??  What is f(h(x)) = ?? Step 1: Set f(x) = zer0 Step 2: Solve for x Step 1: Set f(x) = zer0 Step 2: use TI84+:, enter equation,, Step 3: position cursor at lowest y value Step 4: write down both coordinates, x and y

 Simplifying Expressions w/ Exponents x 2 * x 5  Solving Equations w/Radicals - Irrational Expressions Step 1: Isolate the radical to one side of equation Step 2: Square both sides Step 3: Simplify and solve