Fair Game Review. Chapter 9. Find the square root(s) ± Find the side length of the square. 7. Simplify Simplify 63.

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1 Name Date Chapter 9 Find the square root(s). Fair Game Review ±. Find the side length of the square.. s. s s Area = 9 ft s Area = 0. m 7. Simplif Simplif. 9. Simplif Simplif 88. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 9

2 Name Date Chapter 9 Fair Game Review (continued) Find the side length of the square.. s. s s Area = ft s Area = 9 m Factor the trinomial b + 8b + 8. n + 8n + 9. h h + 7. The surface area (in square inches) of a square card table can be represented b 0 +. a. Write an epression that represents the side length of the table. b. Write an epression for the perimeter of the table. 0 Big Ideas Math Algebra Copright Big Ideas Learning, LLC

3 Name Date 9. Solving Quadratic Equations b Graphing For use with Activit 9. Essential Question How can ou use a graph to solve a quadratic equation in one variable? Earlier in the book, ou learned that the -intercept of the graph of = a + b variables is the same as the solution of a + b = 0. variable The -intercept of the graph of = + is. (, 0) 7 The solution of the equation + = 0 is =. ACTIVITY: Solving a Quadratic Equation b Graphing Work with a partner. a. Sketch the graph of =. b. What is the definition of an -intercept of a graph? How man -intercepts does this graph have? What are the? c. What is the definition of a solution of an equation in? How man solutions does the equation = 0 have? What are the? 7 7 d. Eplain how ou can verif that the -values found in part (c) are solutions of = 0. Copright Big Ideas Learning, LLC Big Ideas Math Algebra

4 Name Date 9. Solving Quadratic Equations b Graphing (continued) ACTIVITY: Solving Quadratic Equations b Graphing Work with a partner. Solve each equation b graphing. a. = 0 b. + = 0 c. + = 0 d. + = Big Ideas Math Algebra Copright Big Ideas Learning, LLC

5 Name Date 9. Solving Quadratic Equations b Graphing (continued) What Is Your Answer?. IN YUR WN WRDS How can ou use a graph to solve a quadratic equation in one variable?. After ou find a solution graphicall, how can ou check our result algebraicall? Use our solutions in Activit as eamples. Copright Big Ideas Learning, LLC Big Ideas Math Algebra

6 Name Date 9. Practice For use after Lesson 9. Solve the equation b graphing. Check our solution(s) = = 0. + = 0. + = 0. 0 = 0. + = 0 7. The height h (in feet) of a javelin thrown at a track and field competition can be modeled b h = t + 0t +, where t is time in seconds. After how man seconds is the javelin 0 feet above the ground? Big Ideas Math Algebra Copright Big Ideas Learning, LLC

7 Name Date 9. Solving Quadratic Equations Using Square Roots For use with Activit 9. Essential Question How can ou determine the number of solutions of a quadratic equation of the form a + c = 0? ACTIVITY: The Number of Solutions of a + c = Work with a partner. Solve each equation b graphing. Eplain how the number of solutions of a c 0 + = Quadratic equation relates to the graph of = a + c. Quadratic function a. = 0 b. + = Copright Big Ideas Learning, LLC Big Ideas Math Algebra

8 Name Date 9. Solving Quadratic Equations Using Square Roots (continued) c. = 0 d. = ACTIVITY: Estimating Solutions Work with a partner. Complete each table. Use the completed tables to estimate the solutions of = 0. Eplain our reasoning. a. b Big Ideas Math Algebra Copright Big Ideas Learning, LLC

9 Name Date 9. Solving Quadratic Equations Using Square Roots (continued) ACTIVITY: Using Technolog to Estimate Solutions Work with a partner. Two equations are equivalent when the have the same solutions. a. Are the equations = 0 and = equivalent? Eplain our reasoning. b. Use the square root ke on a calculator to estimate the solutions of = 0. Describe the accurac of our estimates. c. Write the eact solutions of = 0. What Is Your Answer?. IN YUR WN WRDS How can ou determine the number of solutions of a quadratic equation of the form a + c = 0?. Write the eact solutions of each equation. Then use a calculator to estimate the solutions. a. = 0 b. = 0 c. = 8 Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7

10 Name Date 9. Practice For use after Lesson 9. Solve the equation using square roots.. = = 0. =. 7 = 0. + = 9. + = Solve the equation using square roots. Use a graphing calculator to check our solution(s). 7. ( ) = 9 8. ( ) + = 9. The volume of a shed is 97 cubic feet. Find the width of the shed. 8 ft. ft ft 8 Big Ideas Math Algebra Copright Big Ideas Learning, LLC

11 Name Date 9. Solving Quadratic Equations b Completing the Square For use with Activit 9. Essential Question How can ou use completing the square to solve a quadratic equation? EXAMPLE: Solving b Completing the Square Work with a partner. Five different algebra tiles are shown at the right. Solve + = b completing the square. Step : Use algebra tiles to model the equation + =. Step : Add four ellow tiles to the left side of the equation so that it is a perfect square. Balance the equation b also adding four ellow tiles to the right side. = + + = + ( ) + = Step : Take the square root of each side of the equation and simplif. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 9

12 Name Date 9. Solving Quadratic Equations b Completing the Square (continued) ACTIVITY: Solving b Completing the Square Work with a partner. Write the equation modeled b the algebra tiles. Use algebra tiles to complete the square. Write the solutions of the equation. = Check each solution. ACTIVITY: Writing a Rule Work with a partner. What does this group of tiles represent? How is the coefficient of for this group of tiles related to the coefficient of in the equation from Activit? = How is it related to the number of tiles ou add to each side when completing the square? 0 Big Ideas Math Algebra Copright Big Ideas Learning, LLC

13 Name Date 9. Solving Quadratic Equations b Completing the Square (continued) WRITE A RULE Fill in the blanks. To complete the square, take of the coefficient of the -term and it. this number to each side of the equation. What Is Your Answer?. IN YUR WN WRDS How can ou use completing the square to solve a quadratic equation?. Solve each quadratic equation b completing the square. a. = b. = c. + = Copright Big Ideas Learning, LLC Big Ideas Math Algebra

14 Name Date 9. Practice For use after Lesson 9. Complete the square for the epression. Then factor the trinomial Solve the equation b completing the square.. = = = 8. + = 9. Your backard is rectangular and has an area of 70 square meters. The length of the ard is 8 meters more than the width. Find the length and width of the backard. Big Ideas Math Algebra Copright Big Ideas Learning, LLC

15 Name Date 9. Solving Quadratic Equations Using the Quadratic Formula For use with Activit 9. Essential Question How can ou use the disciminant to determine the number of solutions of a quadratic equation? ACTIVITY: Deriving the Quadratic Formula Work with a partner. The following steps show one method of solving a + b + c = 0. Eplain what was done in each step. a b c + + = 0. Write the equation. 0 a + ab + ac =. a + ab + ac + b = b. a + ab + b = b ac. ( ) a + b = b ac. a + b = ± b ac. a = b ± b ac 7. Quadratic Formula: = b b ac ± a 8. Copright Big Ideas Learning, LLC Big Ideas Math Algebra

16 Name Date 9. Solving Quadratic Equations Using the Quadratic Formula (continued) ACTIVITY: Deriving the Quadratic Formula b Completing the Square Solve a + b + c = 0 b completing the square. (Hint: Subtract c from each side, divide each side b a, and then proceed b completing the square.) Compare this method with the method in Activit. Eplain wh ou think a and b were chosen in Steps and of Activit. ACTIVITY: Writing a Rule Work with a partner. In the quadratic formula in Activit, the epression under the radical sign, b ac, is called the discriminant. For each graph, decide whether the corresponding discriminant is equal to 0, is greater than 0, or is less than 0. Eplain our reasoning. a. rational solution b. rational solutions Big Ideas Math Algebra Copright Big Ideas Learning, LLC

17 Name Date 9. Solving Quadratic Equations Using the Quadratic Formula (continued) c. irrational solutions d. no real solutions What Is Your Answer?. IN YUR WN WRDS How can ou use the discriminant to determine the number of solutions of a quadratic equation?. Use the quadratic formula to solve each quadratic equation. a. + = 0 b. + = 0 c. + + = 0. Use the Internet to research imaginar numbers. How are the related to quadratic equations? Copright Big Ideas Learning, LLC Big Ideas Math Algebra

18 Name Date 9. Practice For use after Lesson 9. Solve the equation using the quadratic formula. Round to the nearest tenth, if necessar = = = = 0. = 9. = 7. + = 0 8. = 9. The deer population in a forest from 000 to 00 can be modeled b = , where is hundreds of deer and is the number of ears since 000. a. When was the deer population about 00? b. Do ou think this model can be used for future ears? Eplain our reasoning. Use the discriminant to determine the number of real solutions of the equation = 0. = = Big Ideas Math Algebra Copright Big Ideas Learning, LLC

19 Name Date Etension 9. Practice For use after Etension 9. Solve the equation using two different methods = 0. + = 0. + =. + = 0 Solve the equation using an method. Eplain our choice of method.. 0 = 0. = = = 0 Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7

20 Name Date Etension 9. Practice (continued) 9. + = 0. + = 9. 0 =. = The height h (in feet) of an arrow shot from a bow can be modeled b h = t + 9t +, where t is time in seconds. a. When will the arrow hit the ground? b. After how man seconds is the arrow feet in the air?. The area of the parking lot is 7 square ards. Find the dimensions of the parking lot. ( ) d d 8 Big Ideas Math Algebra Copright Big Ideas Learning, LLC

21 Name Date 9. Solving Sstems of Linear and Quadratic Equations For use with Activit 9. Essential Question How can ou solve a sstem of two equations when one is linear and the other is quadratic? ACTIVITY: Solving a Sstem of Equations Work with a partner. Solve the sstem of equations using the given strateg. Which strateg do ou prefer? Wh? Sstem of Equations: = + Linear = + Quadratic a. Solve b Graphing 7 Graph each equation and find the points of intersection of the line and the parabola. b. Solve b Substitution Substitute the epression for from the quadratic equation into the linear equation to obtain + = +. Solve this equation and substitute each -value into the linear equation = + to find the corresponding -value. c. Solve b Elimination Eliminate b subtracting the linear equation from the quadratic equation to obtain = + = + 0 = +. Solve this equation and substitute each -value into the linear equation = + to find the corresponding -value. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 9

22 Name Date 9. Solving Sstems of Linear and Quadratic Equations (continued) ACTIVITY: Analzing Sstems of Equations Work with a partner. Match each sstem of equations with its graph. Then solve the sstem of equations. a. = b. = + = = c. = + d. = = = 0 A. B C. D Big Ideas Math Algebra Copright Big Ideas Learning, LLC

23 Name Date 9. Solving Sstems of Linear and Quadratic Equations (continued) What Is Your Answer?. IN YUR WN WRDS How can ou solve a sstem of two equations when one is linear and the other is quadratic?. Summarize our favorite strateg for solving a sstem of two equations when one is linear and the other is quadratic.. Write a sstem of equations (one linear and one quadratic) that has the following number of solutions. a. no solutions b. one solution c. two solutions Your sstems should be different from those in the activities. Copright Big Ideas Learning, LLC Big Ideas Math Algebra

24 Name Date 9. Practice For use after Lesson 9. Solve the sstem b substitution. Check our solution(s).. = +. = + = = +. = =. = = + Solve the sstem b elimination. Check our solution(s).. = = +. = = = 7 = = + = 9. The weekl profit (in dollars) for two street vendors can be modeled b the following equations, where is the number of weeks since the beginning of the ear. = = + 0 When is the weekl profit for each vendor the same? Big Ideas Math Algebra Copright Big Ideas Learning, LLC