What are the parameters of a quadratic model?

This is given in the?formula booklet?as the?axis of symmetry

What can be modelled as a quadratic model?

• These can be used if the graph has a single maximum or minimum
  • H(t) is the vertical height of a football?t?seconds after being kicked
  • A(x) is the area of rectangle of length?x?cm?that can be made with a 20 cm length of string

What are possible limitations of a quadratic model?

• A quadratic has either a maximum or a minimum but?not both
  • This means one end is?unbounded
  • In real-life this might not be the case
  • The function might have both a maximum and a minimum
  • To overcome this you can decide on an appropriate domain so that the outputs are within a range
• Quadratic graphs are?symmetrical
  • This might not be the case in real-life

What are the parameters of a cubic model?

• The?d?represents the value of the function when?x?= 0
  • This is the value of the function when the independent variable is not present
  • This is usually referred to as the initial value
• The?a?has the biggest impact on the rate of change of the function
  • If?a?has a large absolute value then the rate of change varies rapidly
  • If?a?has a small absolute value then the rate of change varies slowly

What can be modelled as a cubic model?

• If the graph of the data has exactly one maximum and one minimum within an interval
• If the graph is monotonic with no maximum or minimum
  • D(t) is the vertical distance below starting point of a bungee jumper?t?seconds after jumping
  • V(x) is the volume of a cuboid of length?x?cmthat can be made with a 200 cm²?of cardboard

What are possible limitations of a cubic model?

• Cubic graphs have?no global maximum or minimum
  • This means the function is?unbounded
  • In real-life this might not be the case
  • The function might have a maximum or minimum
  • To overcome this you can decide on an appropriate domain so that the outputs are within a range