Quadratics

• What is the general form of a quadratic equation?

  y = kx²
• What does the point (0,0) represent in a quadratic graph?

  It is the turning point of the parabola
• What happens to the graph of y = kx² when k < 0?

  The graph is flipped upside down
• If y = kx² and the point (1,5) is on the graph, how do you find k?

  Substitute (1,5) into the equation
• What is the value of k when (1,5) is substituted into y = kx²?

  k = 5
• How do you find the equation of a parabola given the point (1,3)?

  Use y = kx² and solve for k
• What is the value of k when (1,3) is substituted into y = kx²?

  k = 3
• What is the value of k for the point (3,18) in the equation y = kx²?

  k = 2
• What is the value of k when (2,-16) is substituted into y = kx²?

  k = -4
• What is the value of k when (-4,16) is substituted into y = kx²?

  k = 1
• What is the value of k when (4,48) is substituted into y = kx²?

  k = 6
• What is the value of k when (3,36) is substituted into y = kx²?

  k = 4
• What are the steps to find k in a quadratic equation given a point?

  1. Substitute the x and y values into y = kx².
  2. Solve for k.
• What are the characteristics of the graph of y = kx²?

  • Parabola shape
  • Opens upwards if k > 0
  • Opens downwards if k < 0
  • Symmetrical about the y-axis
• What is the equation of the line in the example?

  y = (x - 6)
• When do roots occur in the equation y = (x - 6)?

  When y = 0
• What are the roots of the equation x - 6 = 0?

  x = 6 and x = 12
• What is the y-intercept of the equation y = (x - 6)?

  Occurs when x = 0
• What are the coordinates of the y-intercept for y = (x - 6)?

  (0, 6) and (0, 12)
• What is the product of the roots x = 6 and x = 12?

  72
• What does the symmetry of the graph indicate?

  It is perfectly symmetrical
• What is the value of y when x = 9 in the equation y = (x - 6)?

  y = -9
• What is the first step in sketching the equation (x - 2)(x - 8)?

  x - 2 = 0
• What is the root of the equation x - 2 = 0?

  x = 2
• What are the coordinates of the y-intercept for (x - 2)(x - 8)?

  (0, -2) and (0, -8)
• What is the product of the roots x = 2 and x = 8?

  16
• What is the second step in sketching the equation (x - 2)(x - 8)?

  Find the y-intercept