Solve Quadratic Equations by Finding Square Roots

Slides:



Advertisements
Similar presentations
Examples for Rationalizing the Denominator Examples It is improper for a fraction to have a radical in its denominator. To remove the radical we “rationalize.
Advertisements

1.5 Solving Quadratic Equations by Finding Square Roots
Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x =
EXAMPLE 5 Model a dropped object with a quadratic function
Warm-Up Exercises ANSWER ANSWER x =
Chapter 5 Lesson 3 Solving Quadratic Equations by Finding Square Roots.
Other Types of Equations
EXAMPLE 2 Rationalize denominators of fractions Simplify
5-3 Solving Quadratic Equations by finding Square Roots. Objective: Solve quadratic functions by finding square roots.
5.5 Quadratic Equations Quizzes back TOMORROW…I hope…
5.3 Solving Quadratic Equations by Finding Square Roots (p. 264) How do you simplify radicals? What are the steps to rationalize a denominator? How many.
Radicals without Calculators
5.3 Solving Quadratic Equations by Finding Square Roots.
1. √49 2. –√144 Lesson 4.5, For use with pages
MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of.
Goal: Solving quadratic equations by finding square roots.
5.3: Solving Quadratic Equations by Finding the Square Root Objectives: Students will be able to… Write a square root radical in simplest form Solve a.
Solving Quadratics. Methods for Solving Quadratics Graphing Factoring Square Root Method Completing the Square Quadratic Formula.
5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012.
Name:__________ warm-up Details of the Day EQ: How do we work with expressions and equations containing radicals? I will be able to…. Activities:
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.
The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula.
4.5: Do Now: Review 4.3/4.4. The area of a rectangle with length = 3x + 1 and width = 2x + 1 is 22. Write and solve an equation to find the dimension of.
5.5 Quadratic Equations. Warm-up Factor fully. Solving by Factoring 1a) Solve.
Solve by factoring. x² = - 4 – 5x 2,. Solve by factoring. n² = -30 – 11n -4 and -1.
Find the exact value. 1.) √49 2.) - √ Use a calculator to approximate the value of √(82/16) to the nearest tenth.
Fricovsky 4.5: Do Now: Simplify. 1.
Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.
4.5 “Square Roots”. More Examples Rationalizing the Denominator.
Advanced Algebra Notes Section 4.5: Simplifying Radicals (A) A number r is a _____________ of a number x if. The number r is a factor that is used twice.
Table of Contents Solving Equations That Lead to Quadratic Equations There are several methods one can use to solve a quadratic equation. Sometimes we.
Solving Equations That Lead to Quadratic Equations There are several methods one can use to solve a quadratic equation. Sometimes we are called upon to.
EXAMPLE 5 Model a dropped object with a quadratic function Science Competition For a science competition, students must design a container that prevents.
NOTES 0-5C QUADRATIC FORMULA Student Learning Goals: Students will be able to solve quadratic equations using the quadratic formula.
Section 7.5 Expressions Containing Several Radical Terms
Solve Quadratic Equations by Finding Square Roots
EXAMPLE 2 Rationalize denominators of fractions Simplify
Solving by factoring & taking square roots
Dividing & Solving Equations With Complex Numbers
6.7 Imaginary Numbers & 6.8 Complex Numbers
Section 4.7 Complete the Square.
Use the Quadratic Formula and the Discriminant
Perform Operations with Complex Numbers
Add and Subtract Rational Expressions
Multiply and Divide Rational Expressions
Solving Quadratic Equations by Finding Square Roots
Solve Linear Systems Algebraically (part 2) Elimination
4.5 Solving Quadratic Equations by Finding Square Roots
Graph Simple Rational Functions
Graphing
Solve Systems of Linear Equations in Three Variables
Graph and Write Equations of Hyperbolas
Section 4.3 Solve.
Simplify Complex Rational Expressions
Solve Systems of Linear Inequalities
Review.
Section 4.4 Solve.
Factor & Solve Polynomial Equations
Algebra 12.4 Completing the Square.
Graph Quadratic Equations in Standard form
Quadratic Equations & Square Roots
Warmup Find the exact value. 1. √49 2. –√144.
Section 9.5 Day 1 Solving Quadratic Equations by using the Quadratic Formula Algebra 1.
Warmup Find the exact value. 1. √27 2. –√
Warm Up Linear Relationships Sudoku.
Rational Expressions and Equations
Algebra 1 Section 12.2.
L5-7 Objective: Students will be able to solve quadratics by using the quadratic formula.
Solve Quadratic Equations by Finding Square Roots Lesson 1.5
Do Now 4/12/19 Take out HW from last night. Copy HW in your planner.
Presentation transcript:

Solve Quadratic Equations by Finding Square Roots Section 4.5 Solve Quadratic Equations by Finding Square Roots

California Standard: 8.0: Students solve and graph quadratic equations by factoring or completing the square or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.

OBJECTIVE(S): By following instructions, students will be able to: Use factoring to solve quadratic equations by finding square roots.

Note: Where and

Note: Where and

EXAMPLE 1: Simplify a) b) c) d)

U-TRY#1: Simplify the expression. c) b) d) 7

Def: Rationalizing the Denominator is the process of eliminating a radical from an expression’s denominator. If the denominator has… Then multiply numerator and denominator by:

EXAMPLE 2: Simplify a) b)

EXAMPLE 3: Solve .

EXAMPLE 4: Solve .

U-TRY#2: Simplify the expression (a-b). Solve (c-d). c) b) d) 12

EXAMPLE 5: For a science competition, students must design a container that prevents an egg from breaking when dropped from a height of 50 feet. How long does the container take to hit the ground?

HOMEWORK Sec 4.5 WS