## Solving Quadratic Equations by Factoring

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AP Notes, Outlines, Study Guides, Vocabulary, Practice Exams and more!

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1.07 Algebraic Properties & Equations Essential Questions After completing this lesson, you will be able to answer the following questions: How are algebraic properties applied in the steps to solving equations? How are equations created from context and used to solve real world problems? Main Idea Definition or Summary Example Algebraic Expression An algebraic expression is a ____________ but has nothing to __________. 2x+3 or x ? 4 Create your own: Equation An equation is _____________ set ________ to each other. 2x + 4 = 12 Create your own: Commutative Property of Addition or Multiplication Numbers can change __________. 2+5 = 5+2 3*2 = 2*3 Create your own: Associative Property of Addition or Multiplication The parenthesis move. 1 + (3 + 2) = (1 + 3) + 2

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1.06 Translations Essential Questions After completing this lesson, you will be able to answer these questions: How can translations help me understand how to represent verbal phrases as algebraic expressions? What are the key words and phrases that indicate certain operations? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Translation (Pg. 2) English to Algebra Addition Terms ? ___________ Subtraction Terms ? l__________ Multiplication Terms ? ___________ Division Terms ? ___________ EX: 4 times the difference of n and 8 ___________ EX: The area of a triangle is found by taking half of the product of the base times the height ___________ EX: x more than 5 ___________ EX: 9 subtracted from x ___________ EX: 25% of x ___________

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1.02 Algebraic Expressions Essential Questions After completing this lesson, you will be able to answer the following questions: How do you interpret expressions that represent a quantity in terms of its context? How do you interpret parts of an expression, such as terms, factors, and coefficients? How do you interpret and simplify complicated expressions by viewing one or more of their parts as a single entity? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Algebraic Expressions(P.1) An algebraic expression is an expression that contains one or more numbers, one or more variables, and one or more arithmetic operations. There are 4 boxes of video games. If each box contains x number of games: 4x Vocabulary(P.2): Like __________: have identical variable parts

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02.07 Literal Equations Essential Questions How can you solve linear equations and inequalities in one variable, including equations with coefficients represented by letters? How can you rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations? In the equation: "distance equals rate times time? ____________________ is the most important part. d=(r)(t) In d=(r)(t) the more efficient way to evaluate r is to__________________ it from the rest of the equation first. Work ______________________ to isolate the variable. The key to equations is ________________________.

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02.06 Compound Inequalities Essential Questions How can you create inequalities in one variable and use them to solve problems? How can you represent constraints by inequalities? How can you interpret solutions as viable or nonviable options in a modeling context? Absolute Value Inequalities: Absolute Value Inequalities are problems that involve ranges. For example: On public stairs, handrails must be installed. The height of the handrails must be within a 3 inch range of 35 inches. Compound inequality Key words ?and? / ?or? Scenario 1 A fish has to measure between 18 and 24 inches in length. b>= 18 and b<=24 Writing the compound inequality like this makes it easier to understand that the solutions for b must fall between 18 and 24 inches Scenario 2

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02.05 Inequalities Essential Questions How can you create inequalities in one variable and use them to solve problems? How can you solve linear inequalities in one variable? An?inequality?means the value of the variable is not equal to one number (like in equations), but instead may be greater than or less than a number. There are four primary symbols you need to know when working with inequalities. Indicate what type of circle goes with each inequality symbol > Greater than ______________ < Less than _______________ ? Greater than or equal to ________________ ? Less than or equal to ________________ When you graph an inequality on a number line, there are two questions you must answer. Open or closed circle

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02.03 Absolute Value Equations Essential Questions How can you represent constraints by absolute value equations? How can you interpret solutions as viable or nonviable options in a model? Absolute value equations can have: Examples One solution |x|= ________ Two solutions |x|= ______________________ No solutions |x| = _____________________ To solve an advance absolute value equation e.g. |2x-3|=11 Make two equations to solve by eliminating the absolute signs and making them equal opposite sign answers: Solve below: ___________________ ___________________ Check answers by substituting both into original equation. Check answers below: ____________________________________________ ____________________________________________ You can show constraints in real world problems by:

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02.02 Two-Variable Equations Essential Questions How can we create equations in two or more variables to represent relationships between quantities? How can we represent constraints by equations or inequalities and interpret solutions as viable or nonviable options in the model? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Two-Variable Equations p.2 Steps to solving problems Read and understand the situation within the word problem. Identify and pull out ______________ ______________ from the problem. Assign ____________to unknown values. Set up and solve the equation. Check that your answer makes sense within the context of the problem. Consecutive integer problems p.2 Label the first integer with x, the next with x + 1, the next with x + 2, and so on.

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02.01 One-Variable Equations Essential Questions How can we create equations in one variable and use them to solve problems? How can we solve linear equations in one variable? KEEP IT ___________________. The goal is to figure out how much each x weight weighs. You do this by getting one x on one side and its value on the other side. STEPS TO SOLVING AN EQUATION Simplify each side of the __________________. Get the __________________ on one side of the ___________________. Get the _____________ by ___________________. (Solve for the variable) ___________ your solution. Follow along on page 3, Example 1. ?2(x + 1) = 5x + 4 ? x Simplify each side of the equation. Get the variable on one side of the equation.

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