Standard Algebra – Types of relationships

This lesson comprises six (6) master classes focusing on:

• Models of simultaneous linear equations
• Exponential models
• Quadratic models
• Reciprocal models

Content:

MS-A4.1

• Solve a pair of simultaneous linear equations graphically, by finding the point of intersection between two straight-line graphs, with and without technology
• Develop a pair of simultaneous linear equations to model a practical situation
• Solve practical problems that involve determining and interpreting the point of intersection of two straight-line graphs, including the break-even point of a simple business problem where cost and revenue are represented by linear equations

MS-A4.2

• Use an exponential model to solve problems
  • graph and recognise an exponential function in the form \( y=a^x \) and \( y=a^{−x}\ (a>0) \) where \( k \) is a constant, with and without technology
  • interpret the meaning of the intercepts of an exponential graph in a variety of contexts
  • construct and analyse an exponential model of the form \( y=ka^x \) and \( y=ka^{−x}\ (a>0) \) where \( k \) is a constant, to solve a practical growth or decay problem
• Construct and analyse a quadratic model to solve practical problems involving quadratic functions or expressions of the form \( y=ax^2+bx+c \), for example braking distance against speed
  • recognise the shape of a parabola and that it always has a turning point and an axis of symmetry
  • graph a quadratic function with and without technology
  • interpret the turning point and intercepts of a parabola in a practical context
  • consider the range of values for \( x \) and \( y \) for which the quadratic model makes sense in a practical context
• Recognise that reciprocal functions of the form \( y=\frac{k}{x} \), where \( k \) is a constant, represent inverse variation, identify the rectangular hyperbolic shape of these graphs and their important features
  • use a reciprocal model to solve practical inverse variation problems algebraically and graphically, eg the amount of pizza received when sharing a pizza between increasing numbers of people