Skills Practice Skills Practice for Lesson 3.1

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1 Skills Practice Skills Practice for Lesson. Name Date Lots and Projectiles Introduction to Quadratic Functions Vocabular Define each term in our own words.. quadratic function. vertical motion Problem Set The following rectangles have the same perimeter. Calculate the area of each rectangle... 0 cm 0 cm 5 cm 5. 7 cm 6. 5 cm 7 cm cm cm Chapter Skills Practice 89

2 7. 8 cm cm 8. 8 cm cm cm cm 5 cm 0 cm 0 Write an area function for each rectangle. Use the distributive propert to write the area function without parentheses.. The width of a rectangle is 5 inches longer than its length.. The width of a rectangle is 7 inches longer than its length.. The width of a rectangle is feet shorter than its length.. The width of a rectangle is feet shorter than its length. 5. The length of a rectangle is 6 ards longer than its width. 90 Chapter Skills Practice

3 Name Date 6. The length of a rectangle is ard longer than its width. 7. The length of a rectangle is meters shorter than its width. 8. The length of a rectangle is 0 meters shorter than its width. Use the given area function to answer each question. 9. The area of a square is given b A s, where s is the length of a side. What is the area of a square, if the length of a side is meters? 0. The area of a square is given b A s, where s is the length of a side. What is the area of a square, if the length of a side is meters?. The area of a rectangle is given b A w 0w, where w is the width of the rectangle. What is the area of the rectangle, if the rectangle is 5 ards wide?. The area of a rectangle is given b A w w, where w is the width of the rectangle. What is the area of the rectangle, if the rectangle is 8 ards wide? Chapter Skills Practice 9

4 . The area of a rectangle is given b A l 9l, where l is the length of the rectangle. What is the area of the rectangle, if the rectangle is centimeters long?. The area of a rectangle is given b A l l, where l is the length of the rectangle. What is the area of the rectangle, if the rectangle is 6 centimeters long? Use the given function to answer each question. 5. An arrow is shot directl upward from the ground with an initial velocit of 0 feet per second. The acceleration due to gravit is feet per second squared. The equation s 6t 0t models the height of the arrow after t seconds. How high will the arrow be after seconds? 6. A football is thrown directl upward from the ground with an initial velocit of 0 feet per second. The acceleration due to gravit is feet per second squared. The equation s 6t 0t models the height of the football after t seconds. How high will the football be after second? 9 Chapter Skills Practice

5 Name Date 7. A soccer ball is kicked directl upward from the ground with an initial velocit of 5 feet per second. The acceleration due to gravit is feet per second squared. The equation s 6t t models the height of the soccer ball after t seconds. How high will the soccer ball be after.5 seconds? 8. A basketball is shot directl upward from the ground with an initial velocit of feet per second. The acceleration due to gravit is feet per second squared. The equation s 6t t models the height of the basketball after t seconds. How high will the basketball be after 0.75 seconds? Chapter Skills Practice 9

6 9 Chapter Skills Practice

7 Skills Practice Skills Practice for Lesson. Name Date Intercepts, Vertices, and Roots Quadratic Equations and Functions Vocabular Identif each part from the graph shown. x. coordinates of the vertex. zero(s) of the function. equation of the quadratic function. root(s) of the equation modeled b the graph Chapter Skills Practice 95

8 Problem Set For each quadratic function, complete the table and graph the function. 5. x x 0 6. x x 0 7. x x x 0 96 Chapter Skills Practice

9 Name Date 8. x x x x x Chapter Skills Practice 97

10 0. x 6x x x x x 0. x x x 0 98 Chapter Skills Practice

11 Name Date Identif the x- and -intercepts of each quadratic function x 5 x x x x x x x x x x 5 6 x Chapter Skills Practice 99

12 x x x 6x 8 x 9 Identif the vertex of each quadratic function x x 5 6 x x 5 00 Chapter Skills Practice

13 Name Date x x 7 x x 6 x 6x x 5 x 8x x x 5 6 x Chapter Skills Practice 0

14 Factor each quadratic equation to determine the roots or solutions. 5. x 7x 0 6. x x 0 7. x x x x 0 0. x 7x 0. 6x x 0. 6x x 0. x x 0. 6 x x 0 0 Chapter Skills Practice

15 Skills Practice Skills Practice for Lesson. Name Date Quadratic Expressions Multipling and Factoring Vocabular Give an example of each term.. monomial. binomial. trinomial. difference of two squares Problem Set Complete each multiplication table x x x x x x x x x x x x 7 Chapter Skills Practice 0

16 Calculate each product.. (x )(x ). (x )(x 8). (x )(x ). (x )(x 5) 5. (x )(x 6) 6. ( x )(x 5) 7. (x ) 8. ( x 6) 9. ( x 8 ) ( 0. ( 5 x 7 0 )( 5 6 x ) x ) 0 Chapter Skills Practice

17 Name Date Factor each quadratic expression.. x 8x 5. x 0x. x x 8. x 6x 6 5. x 5x 6. x 7x x x 6 Factor and solve each quadratic equation to determine the root(s). 9. x 7x x x 8 0. x 9x 8 0. x x 0 Chapter Skills Practice 05

18 . x 0. x 0 Determine the zero(s) of each quadratic function. 5. x x 6. x 8x 7. x x 8. x 6x 9 06 Chapter Skills Practice

19 Name Date 9. x 7x 6 0. x 5x 6. 8x. 9x 8 Chapter Skills Practice 07

20 08 Chapter Skills Practice

21 Skills Practice Skills Practice for Lesson. Name Date More Factoring Special Products and Completing the Square Vocabular Explain how each pair of terms is related b identifing similarities and differences.. quadratic equation and perfect square trinomial. trinomial and completing the square Problem Set Factor each quadratic expression.. x 8x 8. x x 9 5. x 0x x x Chapter Skills Practice 09

22 7. x 8. x x 9 0. x 8 Solve each quadratic equation b factoring, if possible.. x 8x 6 0. x 0x 5 0. x 8x 0. x x x 6x 0 6. x 0x Chapter Skills Practice

23 Name Date Solve each quadratic equation b isolating the squared term and taking the square root of both sides. Then solve the equation b factoring to see if ou get the same result. 7. x x x x 69 0 Chapter Skills Practice

24 For each equation of the form x bx c 0, write the value of b or c that would make the expression a perfect square.. x x 0. x x 0. x x 5 0. x x x x 0 6. x 7x 0 Solve each equation b completing the square. 7. x 0x x 6x 0 9. x x 0 0. x x 0 Chapter Skills Practice

25 Name Date. x x 8 0. x x x 5x 0. x 9x 0 Chapter Skills Practice

26 Chapter Skills Practice

27 Skills Practice Skills Practice for Lesson.5 Name Date Quadratic Formula Solving Quadratic Equations Using the Quadratic Formula Vocabular Answer each question about the Quadratic Formula.. What is the Quadratic Formula used for?. Write the Quadratic Formula. Problem Set Solve each equation b completing the square.. x x 0. x 6x x 8x x 0x 0 0 Chapter Skills Practice 5

28 Use the Quadratic Formula to solve each equation. 7. x 5x 0 8. x x x 9x 0 0. x 8x 0. x x 0. x 5x 0 6 Chapter Skills Practice

29 Name Date. 5x 8x 8 0. x x x x 0 Chapter Skills Practice 7

30 8 Chapter Skills Practice

31 Skills Practice Skills Practice for Lesson.6 Name Date Graphing Quadratic Functions Properties of Parabolas Vocabular Write the term that best completes each statement.. The graph of a quadratic equation is called a.. The of a graph is the line that divides the graph into two mirror images.. A is the difference between the rates of change in for a function. Problem Set Complete the table of values for each quadratic function. Then use the table to graph the function.. x x 0 Chapter Skills Practice 9

32 5. x x 0 6. x x 0 7. x x 0 0 Chapter Skills Practice

33 Name Date 8. x x x 0 9. x x x 0 Chapter Skills Practice

34 For each quadratic function, complete the table to calculate the second differences in. 0. x x x x x ( ) 9. x x x x x ( ) 6. x x 5 x x x 5 ( ). x 5x x x 5x ( ) Chapter Skills Practice

35 Name Date Determine the vertex of each parabola x x x x Chapter Skills Practice

36 Determine the x- and -intercepts of each parabola x x x x Chapter Skills Practice

37 Name Date Determine the axis of smmetr of each parabola... 5 x x. 5. x x Chapter Skills Practice 5

38 6 Chapter Skills Practice

39 Skills Practice Skills Practice for Lesson.7 Name Date Graphing Quadratic Functions Basic Functions and Transformations Vocabular Match each function with the description of its graph.. x a. The basic quadratic function. (x ) b. The basic quadratic function moved down units. x c. The basic quadratic function moved left units. x d. The basic quadratic function moved up units 5. (x ) e. The basic quadratic function moved right units Chapter Skills Practice 7

40 Problem Set The graph of the basic quadratic function x and the graph of another quadratic function are shown. Describe the graphical transformations that have been performed on the basic function to result in the graph of the other function x x x 5 x x x x x 8 Chapter Skills Practice

41 Name Date 0.. x x x x Determine the vertex of each quadratic function. First determine the x-value b calculating the average of the zeros. Then use substitution to determine the -value.. x 9x 5 Chapter Skills Practice 9

42 . x 6x 68. x x 0 Chapter Skills Practice

43 Name Date 5. 9x 0x 6 Use the vertex and the shape determined b the value of a to graph each quadratic function. 6. x x 7. x 6x 8 Chapter Skills Practice

44 8. x 8x 8 9. x 0. x x 0. x 8x 8 Chapter Skills Practice

45 Name Date. x 6x. x x 8 Chapter Skills Practice

46 Chapter Skills Practice

47 Skills Practice Skills Practice for Lesson.8 Name Date Three Points Determine a Parabola Deriving Quadratic Functions Vocabular Define each term in our own words.. quadratic function. sstem of equations. trinomial. parabola Chapter Skills Practice 5

48 Problem Set Determine the equation of the parabola that passes through each set of points. 5. (, 5), (, 8), (, ) 6 Chapter Skills Practice

49 Name Date 6. (, ), (, ), (, 0) Chapter Skills Practice 7

50 7. (, ), (, ), (, 8) 8 Chapter Skills Practice

51 Name Date 8. (, ), (, ), (, 5) Chapter Skills Practice 9

52 9. (, 7), (, 6), (, 0) 0 Chapter Skills Practice

53 Name Date 0. (, 6), (, 8), (, ) Chapter Skills Practice

54 . (, ), (, 5), (, 7) Chapter Skills Practice

55 Name Date. (, ), (, 5), (, ) Chapter Skills Practice

56 Chapter Skills Practice

57 Skills Practice Skills Practice for Lesson.9 Name Date The Discriminant The Discriminant and the Nature of Roots/Vertex Form Vocabular Write the term that best completes each statement.. The form a(x h) k is called the of a quadratic equation.. To determine the number and nature of the roots of a quadratic equation, ou can compare its to zero. Problem Set Use the Quadratic Formula to calculate the zero(s) of each quadratic function. Then solve for the average of the zeros to identif each function s vertex and axis of smmetr.. x x. x 6x 9 5. x 6x 5 Chapter Skills Practice 5

58 6. x 8x 7. x 6 8. x 5 Use the discriminant to determine the number of roots/zeros that each equation/function has. 9. x x 0. x x 0. x 0x 5 0. x 6x 6 6 Chapter Skills Practice

59 Name Date. x. x x x x 8x 7. x 8 x x x 0 Complete the square for each function without changing the function. Then determine the vertex. 9. x x 7 0. x 0x 7. x 7. x x 6 Chapter Skills Practice 7

60 . x x. x x Rewrite each quadratic function in vertex form. 5. x 6x 6. x x 7. x 8x 8. x x 5 9. x 0x x 0x 0 8 Chapter Skills Practice

Skills Practice Skills Practice for Lesson 1.1

Skills Practice Skills Practice for Lesson 1.1 Skills Practice Skills Practice for Lesson. Name Date Lots and Projectiles Introduction to Quadratic Functions Vocabular Give an eample of each term.. quadratic function 9 0. vertical motion equation s

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