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Do Now!

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  1. Do Now! sheet Name date date date date date date

  2. Do Now! sheet Name date date date date

  3. Do Now! 10 – 24 - 2013 Factor the trinomial. Factor the trinomial. a) b) ( ) ( ) PRGM FCTPOLY

  4. Do Now! 10 – 24 - 2012 F.O.I.L.( distribute ) Factor the trinomial. c) a) ( ) ( ) b) d)

  5. 10 – 23 - 2012 Do Now! Graph and compare to • Graph • Find Vertex _________ • Identify Axis of Symmetry _________ d) Find “Solutions” x-intercepts __________ e) Opens UP or DOWN f) Compare to y = x 2 Vertex shifts ______ Width _______

  6. 10 – 24 - 2012 Now Graph and compare to • Graph • Find Vertex _________ • Identify Axis of Symmetry _________ d) Find “Solutions” x-intercepts __________ e) Opens UP or DOWN f) Compare to y = x 2 Vertex shifts ______ Width _______

  7. Do Now! Thursday 10 – 25 - 2012 Graph and compare to • Graph • Find Vertex _________ • Identify Axis of Symmetry _________ d) Find “Solutions” x-intercepts __________ e) Opens UP or DOWN f) Compare to y = x 2 Vertex shifts ______ Width _______

  8. Modeling ProjectileObjects When an object is projected, its height h (in feet) above the ground after t seconds can be modeled by the function where is the object’s initial height (in feet). Baseball Hit A baseball is hit by a batter. 1.) Write an equation giving the ball’s height h (in feet) above the ground after t seconds. 2.) Graph the equation. 3.) During what time interval is the ball’s height above 3 feet?

  9. Do Now! 10 – 29 - 2011 Factor the trinomial. 1 a) 2 • Find Vertex _________ • Identify Axis of Symmetry _________ d) Find “Solutions” x-intercepts __________ e) Opens UP or DOWN f) Compare to y = x ( ) ( ) F.O.I.L. 1 b) Rewrite in Quadratic Standard form Vertex shifts ______ Width _______ 1 c)

  10. Do Now! 11 – 29 - 2012 Factor the trinomial. Solve the equation 1) 2) PRGM FCTPOLY PRGM QUAD83 1.6666666666666 1 4 ( x – 2 ) ( 3x + 5 )

  11. 11 – 30 - 2012 Do Now! 1. Solve the equation. 2. Find the x-intercepts. QUAD83 QUAD83 AND 4. What are the Solutions of the equation? 3. Find the Zero’s QUAD83 QUAD83 AND AND

  12. Do Now! Wednesday 10 – 31 - 2012 The Area of the rectangle is 30. What are the lengths of the sides? x 3x + 1 x 3x + 1 ( ) = 30

  13. Modeling ProjectileObjects When an object is projected, its height h (in feet) above the ground after t seconds can be modeled by the function where is the object’s initial height (in feet). Baseball Hit A baseball is hit by a batter. 1.) Write an equation giving the ball’s height h (in feet) above the ground after t seconds. 2.) Graph the equation. 3.) During what time interval is the ball’s height above 3 feet?

  14. Student Modeling DroppedObjects When an object is dropped, its height h (in feet) above the ground after t seconds can be modeled by the function where is the object’s initial height (in feet). CLIFF DIVING A cliff diver dives off a cliff 40 feet above water. 1.) Write an equation giving the diver’s height h (in feet) above the water after t seconds. 2.) Graph the equation. (plot some points from the table) 3.) How long is the diver in the air? (what are you looking for?) 4.) The place that the diver starts is called what? (mathematically) 5.) What are we going to count by? Window re-set…. Xmin = Xmax = Xscl = Ymin = Ymax = Yscl = HEIGHT TIME

  15. Student Modeling DroppedObjects When an object is dropped, its height h (in feet) above the ground after t seconds can be modeled by the function where is the object’s initial height (in feet). CLIFF DIVING A cliff diver dives off a cliff 40 feet above water. 1.) Write an equation giving the diver’s height h (in feet) above the water after t seconds. 2.) Graph the equation. (plot some points from the table) 3.) How long is the diver in the air? (what are you looking for?) 4.) The place that the diver starts is called what? (mathematically) 5.) What are we going to count by? Window re-set…. Xmin = Xmax = Xscl = Ymin = Ymax = Yscl = HEIGHT TIME

  16. 40 30 20 HEIGHT 10 5 0.5 1.5 1 TIME

  17. Modeling Dropped Objects When an object is dropped, its height h (in feet) above the ground after t seconds can be modeled by the function where is the object’s initial height (in feet). CLIFF DIVING A cliff diver dives off a cliff 40 feet above water. 1.) Write an equation giving the diver’s height h (in feet) above the water after t seconds. 2.) Graph the equation. 3.) How long is the diver in the air?

  18. Modeling Dropped Objects When an object is dropped, its height h (in feet) above the ground after t seconds can be modeled by the function HEIGHT where is the object’s initial height (in feet). Let’s assume that the cliff is 40 feet high. TIME

  19. Let’s assume that the cliff is 40 feet high. Write an equation? Make the substitution. HEIGHT Graph it. TIME

  20. 40 Let’s assume that the cliff is 40 feet high. Write an equation? 30 Make the substitution. 20 Graph it. HEIGHT 5 1 .5 1.5 TIME seconds

  21. 40 Let’s assume that the cliff is 40 feet high. Write an equation? 30 Make the substitution. 20 Graph it. HEIGHT How long will the diver be in the air? 5 Think about… what are we trying to find? 1 Hint: we want SOLUTIONS. .5 1.5 +1.58 seconds -1.58 seconds TIME

  22. Changing the world takes more than everything any one person knows. But not more than we know together. So let's work together.

  23. 11 – 8 - 2012 Do Now! Quadratic Formula Example 1) Solve using the Quadratic Formula Identify: A: B: C: 1 2 12 Plug them in to the formula

  24. How to use a Discriminant to determine the number of solutions of a quadratic equation. discriminant *if , (positive) then 2 real solutions. *if , (zero) then 1 real solutions. *if , (negative) then 2 imaginary solutions.

  25. MONDAY , NOV. 7th ASSIGNMENT PAGE 279 # 12 -27 ALL Complex Numbers ( i ) PAGE 296 # 3 – 6, 31 – 33, 40 - 42, Quadratic Formula QUAD83 Solve the equation Discriminant How many solutions

  26. Collaborative Activity Sheet 1 Chapter 4 Solving – Graphing Quadratic functions Collaborative Activity Sheet Chapter 4 Solving – Graphing Quadratic functions A.) For a science competition, students must design a container that prevents an egg from breaking when dropped from a height of 50 feet. 1.) Write an equation giving the container’s height (h) above the ground after (t) seconds. 2.) Graph the equation. 3.) How long does the container take to hit the ground? A.) For a science competition, students must design a container that prevents an egg from breaking when dropped from a height of 50 feet. 1.) Write an equation giving the container’s height (h) above the ground after (t) seconds. 2.) Graph the equation. 3.) How long does the container take to hit the ground? B.) A bird flying at a height of 30 feet carries a shellfish. The bird drops the shellfish to break it and get the food inside. 1.) Write an equation giving the shellfish height (h) above the ground after (t) seconds. 2.) Graph the equation. 3.) How long does the shellfish take to hit the ground? B.) A bird flying at a height of 30 feet carries a shellfish. The bird drops the shellfish to break it and get the food inside. 1.) Write an equation giving the shellfish height (h) above the ground after (t) seconds. 2.) Graph the equation. 3.) How long does the shellfish take to hit the ground? C.) Some harbor police departments have firefighting boats with water cannons. The boats are use to fight fires that occur within the harbor. The function y = - 0.0035x( x – 143.9) models the path of water shot by a water cannon where x is the horizontal distance ( in feet ) and y is the corresponding height ( in feet ). 1.) Write an equation (in standard form) modeling the path of water. 2.) Graph the equation. 3.) How far does the water cannon shoot? C.) Some harbor police departments have firefighting boats with water cannons. The boats are use to fight fires that occur within the harbor. The function y = - 0.0035x( x – 143.9) models the path of water shot by a water cannon where x is the horizontal distance ( in feet ) and y is the corresponding height ( in feet ). 1.) Write an equation (in standard form) modeling the path of water. 2.) Graph the equation. 3.) How far does the water cannon shoot? D.) A football is kicked upward by a player in the game. The height h (in feet) of the ball after t seconds is given by the function Where v (the velocity for the ball when kicked) is 96 mph, the initial height of the ball is 3 feet. 1.) Write an equation giving the ball’s height (h) above the ground after (t) seconds. 2.) Graph the equation. 3.) How long does it take for the ball to hit the ground? D.) A football is kicked upward by a player in the game. The height h (in feet) of the ball after t seconds is given by the function Where v (the velocity for the ball when kicked) is 96 mph, the initial height of the ball is 3 feet. 1.) Write an equation giving the ball’s height (h) above the ground after (t) seconds. 2.) Graph the equation. 3.) How long does it take for the ball to hit the ground?

  27. Collaborative Activity Sheet 2 Chapter 4 Solving – Graphing Quadratic functions A.) For a science competition, students must design a container that prevents an egg from breaking when dropped from a height of 50 feet. 1.) Write an equation giving the container’s height (h) above the ground after (t) seconds. 2.) Graph the equation. 3.) How long does the container take to hit the ground? E.) A stunt man working on a movie set falls from a window that is 70 feet above an air cushion positioned on the ground. 1.) Write an equation that models the height of the stunt man as he falls. 2.) Graph the equation. 3.) How long does it take him to hit the ground? F.) A science center has a rectangular parking lot. The Science center wants to add 18,400 square feet to the area of the parking lot by expanding the existing parking lot as shown 1.) Find the area of the existing parking lot. 2.) Write an equation that you can use to find the value of x 3.) Solve the equation. By what distance x should the length and width of the parking lot be expanded? B.) A bird flying at a height of 30 feet carries a shellfish. The bird drops the shellfish to break it and get the food inside. 1.) Write an equation giving the shellfish height (h) above the ground after (t) seconds. 2.) Graph the equation. 3.) How long does the shellfish take to hit the ground? x 270 150 C.) Some harbor police departments have firefighting boats with water cannons. The boats are use to fight fires that occur within the harbor. The function y = - 0.0035x( x – 143.9) models the path of water shot by a water cannon where x is the horizontal distance ( in feet ) and y is the corresponding height ( in feet ). 1.) Write an equation (in standard form) modeling the path of water. 2.) Graph the equation. 3.) How far does the water cannon shoot? x G.) An object is propelled upward from the top of a 300 foot building. The path that the object takes as it falls to the ground can be modeled by Where t is the time (in seconds) and y is the corresponding height ( in feet) of the object. 1.) Graph the equation. 2.) How long is it in the air? D.) A football is kicked upward by a player in the game. The height h (in feet) of the ball after t seconds is given by the function Where v (the velocity for the ball when kicked) is 96 mph, the initial height of the ball is 3 feet. 1.) Write an equation giving the ball’s height (h) above the ground after (t) seconds. 2.) Graph the equation. 3.) How long does it take for the ball to hit the ground?

  28. Collaborative Activity Sheet 3 Chapter 4 Solving – Graphing Quadratic functions 1.) A football is kicked upward by a player in the game. The height h (in feet) of the ball after t seconds is given by the function Where v (the velocity for the ball when kicked) is 65 mph, the initial height of the ball is 3 feet. a.) Write an equation giving the ball’s height (h) above the ground after (t) seconds. b.) Graph the equation. c.) How long does it take for the ball to hit the ground? d.) Is the Vertex a Max or Min? 3.) In a football game, a defensive player jumps up to block a pass by the opposing team’s quarterback. The player bats the ball downward with his hand at an initial vertical velocity of -50 feet per second when the ball is 7 feet above the ground. How long do the defensive player’s teammates have to intercept the ball before it hits the ground? x 270 4.) The aspect ratio of a widescreen TV is the ratio of the screen’s width to its height, or 16:9 . What are the width and the height of a 32 inch widescreen TV? (hint: Use the Pythagorean theorem and the fact that TV sizes such as 32 inches refer to the length of the screen’s diagonal.) Draw a picture. 150 x 2.) A science center has a rectangular parking lot. The Science center wants to add 18,400 square feet to the area of the parking lot by expanding the existing parking lot as shown a.) Find the area of the existing parking lot. b.) Write an equation that you can use to find the value of x c.) Solve the equation. By what distance x should the length and width of the parking lot be expanded? 5.) You are using glass tiles to make a picture frame for a square photograph with sides 10 inches long. You want to frame to form a uniform border around the photograph. You have enough tiles to cover 300 square inches. What is the largest possible frame width x? x x x x

  29. Graph and compare to • Graph • Find Vertex • Identify Axis of Symmetry d) Find “Solutions” x-intercepts e) Opens UP or DOWN f) Compare to y = x 2

  30. Graph and compare to • Graph • Find Vertex • Axisof Symmetry d) x-intercepts e) Opens UP or DOWN f) Compare to y = x 2

  31. Graph and compare to • Graph • Find Vertex • Axisof Symmetry d) x-intercepts e) Opens UP or DOWN f) Compare to y = x 2

  32. Graph and compare to • Graph • Find Vertex • Axisof Symmetry d) x-intercepts e) Opens UP or DOWN f) Compare to y = x 2

  33. Graph and compare to • Graph • Find Vertex • Axisof Symmetry d) x-intercepts e) Opens UP or DOWN f) Compare to y = x 2

  34. Graph and compare to • Graph • Find Vertex • Identify Axis of Symmetry d) Find “Solutions” x-intercepts e) Opens UP or DOWN f) Compare to y = x 2

  35. Graph and compare to • Graph • Find Vertex • Identify Axis of Symmetry d) Find “Solutions” x-intercepts e) Opens UP or DOWN f) Compare to y = x 2

  36. Graph and compare to • Graph • Find Vertex • Identify Axis of Symmetry d) Find “Solutions” x-intercepts e) Opens UP or DOWN f) Compare to y = x 2

  37. Graph and compare to • Graph • Find Vertex • Identify Axis of Symmetry d) Find “Solutions” x-intercepts e) Opens UP or DOWN f) Compare to y = x 2

  38. Graph and compare to Axis of Symmetry (1, 3) • Graph • Find Vertex • Identify Axis of Symmetry d) Find “Solutions” x-intercepts e) Opens UP or DOWN f) Compare to y = x vertex x-intercepts 2 x = 1

  39. Graph and compare to Axis of Symmetry • Graph • Find Vertex • Identify Axis of Symmetry d) Find “Solutions” x-intercepts e) Opens UP or DOWN f) Compare to y = x x-intercepts (1, -4) vertex 2 x = 1

  40. Graph and compare to • Graph • Find Vertex _________ • Identify Axis of Symmetry _________ d) Find “Solutions” x-intercepts __________ e) Opens UP or DOWN f) Compare to y = x 2 Vertex shifts ______ Width _______

  41. Quiz 4.1 Graph and compare to • Graph • Find Vertex _________ • Identify Axis of Symmetry _________ d) Find “Solutions” x-intercepts __________ e) Opens UP or DOWN f) Compare to y = x 2 Vertex shifts ______ Width _______

  42. Quiz 4.1 RETAKE Graph and compare to • Graph • Find Vertex _________ • Identify Axis of Symmetry _________ d) Find “Solutions” x-intercepts __________ e) Opens UP or DOWN f) Compare to y = x 2 Vertex shifts ______ Width _______

  43. Quiz 4.1 RETAKE Graph and compare to • Graph • Find Vertex _________ • Identify Axis of Symmetry _________ d) Find “Solutions” x-intercepts __________ e) Opens UP or DOWN f) Compare to y = x 2 Vertex shifts ______ Width _______

  44. Quiz 4.2 Graph and compare to #1) • Graph • Find Vertex _________ • Identify Axis of Symmetry _________ d) Find “Solutions” x-intercepts __________ e) Opens UP or DOWN f) Compare to y = x 2 Vertex shifts ______ Width _______

  45. Graph and compare to #2) • Graph • Find Vertex _________ • Identify Axis of Symmetry _________ d) Find “Solutions” x-intercepts __________ e) Opens UP or DOWN f) Compare to y = x 2 Vertex shifts ______ Width _______

  46. 4.1 Graphing Quadratic Functions Whatyou should learn: Goal 1 Graph quadratic functions. Goal 2 Use quadratic functions to solve real-life problems. 4.1 Graphing Quadratic Functions in Standard Form

  47. Vocabulary Quadratic Functions in Standard Form is written as ,Where a ¹ 0 A parabola is the U-shaped graph of a quadratic function. The vertex of a parabola is the lowest point of a parabola that opens up, and the highest point of a parabola that opens down. 4.1 Graphing Quadratic Functions in Standard Form