IB DP Maths: AI SL复习笔记2.2.3 Properties of Graphs

What are the key features of quadratic graphs?

• • If a is positive then the vertex is the minimum point
  • If a is negative then the vertex is the maximum point

What are the key features of cubic graphs?

These can be found using your GDC

• • These are also called the x-intercepts
  • There can be 1, 2 or 3 x-intercepts
    • There is always at least 1
• There are either 0 or 2 local minimums/maximums
  • If there are 0 then the curve is monotonic (always increasing or always decreasing)
  • If there are 2 then one is a local minimum and one is a local maximum

What are the key features of exponential graphs?

• The coefficient of x and the constant k determine whether the graph is increasing or decreasing
  • If the coefficient of x and k have the same sign then graph is increasing
  • If the coefficient of x and k have different signs then the graph is decreasing
• There is at most 1 root
  • It can be found using your GDC

What are the key features of sinusoidal graphs?

• The maximum value is y = a + d
• The minimum value is y = -a + d
• The principal axis is the horizontal line halfway between the maximum and minimum values
  • This is y = d
• The amplitude is the vertical distance from the principal axis to the maximum value
  • This is a