Turning Point

• What is a vertex in graphing?

  Turning point of a graph
• What does the vertex indicate about a graph?

  It shows where the graph changes direction
• What is the equation given in the video?

  y = x² - 6x + 11
• How do you complete the square for the equation?

  Rewrite as y = (x - 3)² + 2
• Why is the completed square form useful?

  It helps find the vertex coordinates easily
• What are the coordinates of the vertex for the equation?

  (3, 2)
• Why is 2 the lowest y-coordinate?

  Because square numbers are non-negative
• What is the opposite sign of -3 in the bracket?

  3
• What happens when you square a number?

  It becomes positive or zero
• How do you find the vertex from the completed square form?

  Use the opposite sign of the bracket number
• What is the process to find the vertex from the completed square form?

  1. Identify the number in the bracket.
  2. Take the opposite sign for x-coordinate.
  3. Use the final term for y-coordinate.
• What is the vertex for the equation y = x² + 8x + 18?

  (-4, 2)
• What is unique about the vertex of y = -x² + 2x + 4?

  It has a maximum point
• How do you factor out a negative from an equation?

  Change the signs of each term inside
• What is the vertex for the equation y = 2x² - 12x + 13?

  (3, -5)
• What are the steps to complete the square for y = 2x² - 12x + 13?

  1. Factor out the coefficient of x².
  2. Complete the square inside the bracket.
  3. Expand and simplify.
  4. Identify the vertex coordinates.
• What is the final form of the equation after completing the square?

  y = 2(x - 3)² - 5
• What does the coefficient in front of x² affect?

  It affects the graph's direction and width
• How does the vertex change with different coefficients?

  It can change from minimum to maximum
• What is the vertex for the equation y = -x² + 4x + 5?

  (2, 9)
• What is the final vertex for y = 2(x - 3)² - 5?

  (3, -5)
• Why is it important to understand the vertex of a quadratic function?

  It helps in graphing and analyzing the function
• How can you quickly find the vertex from the completed square form?

  Identify the bracket number and adjust signs