Class Greeting.

Slides:



Advertisements
Similar presentations
7.1 – Completing the Square
Advertisements

2-4 completing the square
Solving Quadratic Equations by Completing the Square
Solving Quadratic Equations by the Quadratic Formula
CHAPTER 7-1 SOLVING SYSTEM OF EQUATIONS. WARM UP  Graph the following linear functions:  Y = 2x + 2  Y = 1/2x – 3  Y = -x - 1.
Class Greeting. Chapter 8 Systems of Linear Equations and Inequalities Lesson 8-1a Solving Systems Equations by Graphing 1.Determine if a system of equations.
EXAMPLE 2 Rationalize denominators of fractions Simplify
Zero – product property
Example 2-1c *****STATE ALL EXCLUDED VALUES***** a. Find b. Find a.Find b.Find Review: 7.2a Mini-Quiz.
A manufacturer has a setup cost of $2000 for the production of a new football. The cost of labor and materials for producing each unit is $15. (a) Write.
Lesson 3 Contents Example 1Radical Equation with a Variable Example 2Radical Equation with an Expression Example 3Variable on Each Side.
Using square roots to solve quadratic equations. 2x² = 8 22 x² = 4 The opposite of squaring a number is taking its square root √ 4= ± 2.
Get out Homework 9-6 Practice B Answers , , 2.48
5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012.
Solve: The length of a rectangular picture frame is 4 inches less than its width. The area of the picture frame is 320 square inches. Find the dimensions.
Factor. 1)x² + 8x )y² – 4y – 21. Zero Product Property If two numbers multiply to zero, then either one or both numbers has to equal zero. If a.
Unit 7 Quadratics Radical Equations Goal: I can solve simple radical equations in one variable (A-REI.2)
Review: 6.5f Mini-Quiz 1. Solve: Verify by factoring. 2. Solve by Graphing: y = x 2 – 4x. Verify by factoring.
8-1 Completing the Square
Do Now 1) Factor. 3a2 – 26a + 35.
Solving Systems of Equations: The Elimination Method Solving Systems of Equations: The Elimination Method Solving Systems of Equations: The Elimination.
2.1 – Linear and Quadratic Equations Linear Equations.
5-7: COMPLEX NUMBERS Goal: Understand and use complex numbers.
Review: 6.5e Mini-Quiz 1. Solve: 16x 2 – 24x = – 4x Solve: (x – 3)(x – 2) = 30.
6.4 Completing the Square The Square Root Property.
Splash Screen. Then/Now You solved quadratic equations by completing the square. Solve quadratic equations by using the Quadratic Formula. Use the discriminant.
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.
5.9 Complex Numbers Alg 2. Express the number in terms of i. Factor out –1. Product Property. Simplify. Multiply. Express in terms of i.
Algebra 2 Solving Radical Equations Section 7-5 Solving Square Root and Other Radical Equations Lesson 7-5.
Factor: 1. 2x 2 – 3x x 2 - 8x x 2 – 10x – 20.
SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE
EXAMPLE 2 Rationalize denominators of fractions Simplify
Solving Quadratic Equations by the Complete the Square Method
Warm-Up.
Solve a quadratic equation
A quadratic equation is written in the Standard Form,
10.7 Solving Quadratic Equations by Completing the Square
Class Greeting.
Solving Quadratic Equations by Factoring
The Quadratic Formula and the Discriminant
Class Greeting.
Review: 6.5b Mini-Quiz 1. Solve: 9x2 – 100 = 0.
Review: Simplify.
Review: 8.2b Mini-Quiz Find an equation of the line with slope m = 1 and passing through the intersection of the lines x + 7y = 6 and -3x + y = 4.
Solving One and Two Step Equations
Warmup Find the exact value. 1. √27 2. –√
Quadratic Equations.
Review: 8.1a Mini-Quiz Graph the systems of equations. Then determine whether each system has no solution, one solution, or infinitely many solutions.
Warm Up #3 Find the exact value. 2. –√ √49 ANSWER –12 7 ANSWER
Algebra 1 Section 12.3.
Review: 10.1a Mini-Quiz 1. Solve 5y = 125y2
Review: 8.3a Mini-Quiz Use elimination to solve the system of equations. 4 x + 3y = x + 3y = 0 Use elimination to solve the system of equations.
Review: 10.3a Mini-Quiz Solve by using the Quadratic Formula.
Review: 8.5b Mini-Quiz A person plans to invest up to $10,000 in two different interest-bearing accounts, account X and account Y. Account Y is to contain.
Example 2B: Solving Linear Systems by Elimination
Class Greeting.
Review: 9.3a Mini-Quiz Simplify . Simplify.
Review: 10.2b Mini-Quiz The revenue R (in dollars) from selling x units of an infant stroller is modeled by
Review: 6.5c Mini-Quiz 1. Solve: 4x2 – 40 = –27x.
Review: 10.1b Mini-Quiz Five hundred dollars ($500) is deposited in an account. At the end of 2 years, the balance in the account is $605. The interest.
Review: 8.2a Mini-Quiz 1. Use substitution to solve the system of equations. 2. Use substitution to solve the system of equations. 3. Use substitution.
Class Greeting.
Review: 9.3c Mini-Quiz Simplify 108 − Simplify.
Solving Quadratic Equations by Finding Square Roots
Review: 6.5d Mini-Quiz 1. Solve: 9x2 + 12x + 4 = 0.
8.2 Mini-Quiz Review: 6.5a Mini-Quiz Solve Solve.
Class Greeting.
Warm UP Simplify      .
Equations Involving Absolute Value
Presentation transcript:

Class Greeting

Chapter 10 Quadratic Equations and Functions Lesson 10-1a Solving Quadratic Equations by Factoring and using the Square Root Property

Objective: Students will solve quadratic equations by factoring and by using the square root property.

Solving Quadratic Equations by Factoring

Solve Then check the solutions. – 4y = 0 4y(3y – 1) = 0 3y – 1 = 0 or Answer: y = 0, 3 Example 2-5a

Solve = 0 = (2xy -2y) + (7x – 7) = 0 = 0 = 0 Answer: y = - 7 2 and x = 1 Example 2-2a

Solve by grouping. a = 15 and c = –8 therefore ac = –120 What 2 numbers multiply to make -120 and add to make –14? 6 and –20 Replace -14b with 6b – 20b Group 15b2 + 6b – 20b – 8 = 0 (15b2 + 6b) – 1(20b + 8) = 0 3b(5b + 2) – 4(5b + 2) = 0 6b –20b –14b TRUE

Now that the equation is factored, SOLVE IT. Answer: The solution set is b = Check your answers. Example 4-4a

The Square Root Property

The solutions are x = 3 and x = - 3 . Solve 4x2 = 12 by the Square Root Property. x2 = 3 𝑥 2 = 3 x = ± 3 The solutions are x = 3 and x = - 3 . Check these in the original equation.

Solve (3x + 5)2 – 16 = 0 by the Square Root Property. 𝑥=− 5 3 ± 4 3 The solutions are x = - 1 3 and x = -3. Check these in the original equation.

Lesson Summary: Objective: Students will solve quadratic equations by factoring and by using the square root property.

Preview of the next Lesson: Objective: Students will solve word problems by solving quadratic equations by factoring and using the square root property.

Homework 553+554/1,9,17...81

Stand Up Please