Quadratic Inequalities

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TEKS FCUS - Quadratic Inequalities VCABULARY TEKS ()(H) Solve quadratic inequalities. TEKS ()(E) Create and use representations to organize, record, and communicate mathematical ideas.

ESSENTIAL UNDERSTANDING You can solve quadratic inequalities algebraicall, graphicall, or using a table, b identifing the linear factors or zeros of the related function, and analzing the values of

1 TEKS FCUS - Quadratic Inequalities VCABULARY TEKS ()(H) Solve quadratic inequalities. TEKS ()(E) Create and use representations to organize, record, and communicate mathematical ideas. Representation a wa to displa or describe information. You can use a representation to present mathematical ideas and data. ESSENTIAL UNDERSTANDING You can solve quadratic inequalities algebraicall, graphicall, or using a table, b identifing the linear factors or zeros of the related function, and analzing the values of around zero. Problem Solving Inequalities Algebraicall Solve each inequalit algebraicall. A * ( - 7) Factor. How can ou check that the answer is reasonable? Check a value of in this range. For eample, for = 3, (3) - (3) = -, which is less than, so the answer is reasonable. 7 and ( - 7), or and ( - 7) 7 7 and 7, or and 7 7 The product is negative, so the two factors must have different signs. Simplif. 7 No value can be both greater than 7 and less than. B + ( - 7) 7 7 and ( - 7) 7, or and ( - 7) 7 and 7 7, or and 7 Factor. The product is positive, so the two factors must have the same signs. Simplif. 7 7 or Combine the and inequalities into one inequalit each. 8 Lesson - Quadratic Inequalities

Problem Solving Inequalities Using a Table Solve the inequalit + * using a table. How should ou choose the -values for the table? The graph of the function = - + is a parabola.

2 Problem Solving Inequalities Using a Table Solve the inequalit + * using a table. How should ou choose the -values for the table? The graph of the function = - + is a parabola. It is often helpful to choose values of on either side of the verte of the parabola. Step Step Make a table of values Analze the values in the table. Use what ou know about the smmetr of the graph of = - + to help ou. When, the value of decreases, reaches a minimum of - at = 3, and then increases. The -values in the table for which - + is negative are between and, so the solution of the inequalit - + is. Problem 3 TEKS Process Standard ()(E) Solving Inequalities Using a Graph Find the solution sets for ( ) + and ( ) *. Graph the corresponding function f () = ( - ) - and look for where the graph is above or below the -ais. The solution set for ( - ) - 7 is all -values of points on the parabola that lie above the -ais. How do ou find the -intercepts of the graph? Solve the related quadratic equation, ( - ) - =, to find that the -intercepts are (, ) and (, ). or 7 The solution set for ( - ) - is all -values of points on the parabola that lie below the -ais. PearsonTEXAS.com 9

3 Problem TEKS Process Standard ()(A) Appling Quadratic Inequalities A metal arch in a sculpture garden is modeled b the function = + 8, where is the height of the arch in feet and is the horizontal distance in feet from one end of the arch. For what distances from the end of the arch is the height of the arch less than feet? What does the graph look like? Since the coefficient of is less than zero, the graph of the function = is a parabola that opens downward. Step Step Step 3 Step Write a quadratic inequalit or Solve the corresponding equation. First find the values of where equals = - ( - + 3) = - ( - )( - 3) = = or = 3 Interpret the solution. The graph of = opens downward and crosses the -ais at = and = 3. The solution of is or In this situation, the domain of the original function, = - + 8, is. So, the distances from the end of the arch for which the height of the arch is less than feet are and 3. Check. Use a graph to check. The graph shows = and = in the viewing window and. Lesson - Quadratic Inequalities

NLINE H M E W R K PRACTICE and APPLICATIN EXERCISES Scan page for a Virtual Nerd tutorial video. Solve each inequalit. For additional support when completing our homework, go to PearsonTEXAS.com.. - 3.

4 NLINE H M E W R K PRACTICE and APPLICATIN EXERCISES Scan page for a Virtual Nerd tutorial video. Solve each inequalit. For additional support when completing our homework, go to PearsonTEXAS.com Ú Ú ( + ) - 8. ( - ) Match each inequalit with the correct graph A. B. C The function = - + models the profit in dollars earned b a tour guide when people sign up for a tour. a. How man people need to sign up for a tour in order for the profit to be at least $7? b. How man people need to sign up for a tour in order for the profit to be more than $? c. Is it possible for the tour guide to lose mone (make a negative profit) on a tour? Eplain. 7. A friend plans to use feet of fencing to surround three sides of a rectangular vegetable garden. The fourth side of the vegetable garden is bordered b a wall. a. Write a function that models the area A of the vegetable garden in square feet when the length of the fence perpendicular to the wall is feet. b. For what lengths is the area of the vegetable garden greater than square feet? c. For what lengths is the area of the vegetable garden greater than 3 square feet? d. Is it possible for the fence to enclose an area greater than feet? Eplain. 8. Use Multiple Representations to Communicate Mathematical Ideas ()(D) Use algebraic methods, a table, and a graph to eplain wh the inequalit has no solutions. 9. Eplain Mathematical Ideas ()(G) A student solved the inequalit He said that the same solution set must also be the solution set for since he multiplied both sides of the inequalit b -. Do ou agree with the student? Wh or wh not? PearsonTEXAS.com

5 Determine whether each statement is alwas, sometimes, or never true.. The inequalit + b 7 has a solution.. The inequalit + b has a solution.. If the graph of = a + b + c intersects the -ais, then the inequalit a + b + c has a solution. 3. If the graph of = a + b + c intersects the -ais, then the inequalit a + b + c has a solution.. If a, then the inequalit ( - ) + 3 a has a solution. The table below represents data for a quadratic function. Use the table for Eercises Use the table to determine the values of for which Use the table to determine the values of for which. 7. Eplain how ou know that there are no values of for which. 8. Analze Mathematical Relationships ()(F) Write a quadratic inequalit of the form a + b + c that has the solution set 3. (Hint: Consider the values of that must be zeros of the related quadratic function.) TEXAS Test Practice 9. Which of the following values is in the solution set of the inequalit - 3 -? A. - B. -7 C. 8 D Which inequalit has a solution of the form a b? F H G J How man integers are solutions of the inequalit + -? A. 7 B. 8 C. 9 D. 3. Which inequalit has no solutions? F. ( - 3) - H. ( - 3) + G. ( - 3) - 7 J. ( - 3) + 7 Lesson - Quadratic Inequalities

2-3. Attributes of Absolute Value Functions. Key Concept Absolute Value Parent Function f (x)= x VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING

2-3. Attributes of Absolute Value Functions. Key Concept Absolute Value Parent Function f (x)= x VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING - Attributes of Absolute Value Functions TEKS FOCUS TEKS ()(A) Graph the functions f() =, f() =, f() =, f() =,f() = b, f() =, and f() = log b () where b is,, and e, and, when applicable, analze the ke