Activities Proficiencies Understanding through connecting the x-axis The graph of the parabola . intercepts of a graph to the related linear factors Using technology to explore families of graphs, including and the related equation. simple transformations of : graphs of the form , . Fluency through plotting points accurately and Graphs of that can be expressed in the form , where p and q sketching graphs from equations and labelling are integers. Use technology to explore patterns to assist key features. with finding the values of p and q. Problem solving through recognising that every quadratic graph is a transformation of , The connection between linear factors, solutions to the and using this knowledge as an aid for equation and the x-axis intercepts of the graph of . sketching parabolas from their equations. Graphs of the form and , as a translation of and as a special Reasoning through explaining how different case of . equivalent forms of an equation highlight Using technology to explore graphs of the form ; the different features of the corresponding graph. coordinates of the vertex and the axis of symmetry. Considering different levels of student ability Level 8 Students who are working at this level could: Explore the relationship between simple quadratic sequences defined by tables of values with a constant second difference and the corresponding parabolic graphs. Level 10 Students who are working at this level could: Use graphical guess – check and refine method to identify a sequence of nested intervals containing a solution for equations of the form: quadratic = constant, quadratic = linear and quadratic = quadratic. Assessment ideas Students carry out an investigation where they explore possible equations of real world objects that can be modelled with a quadratic function, such as the arch of a bridge and the curve formed by a chain hanging between two posts. Resources AMSI NCTM Illuminations CIMT FUSE: Discover resources aligned to the Victorian Curriculum Notes
Activities Proficiencies The graph of the parabola . Using technology to explore families of graphs, including simple transformations of : graphs of the form , . Graphs of that can be expressed in the form , where p and q are integers. Use technology to explore patterns to assist with finding the values of p and q. The connection between linear factors, solutions to the equation and the x-axis intercepts of the graph of . Graphs of the form and , as a translation of and as a special case of . Using technology to explore graphs of the form ; the coordinates of the vertex and the axis of symmetry. Understanding through connecting the x-axis intercepts of a graph to the related linear factors and the related equation. Fluency through plotting points accurately and sketching graphs from equations and labelling key features. Problem solving through recognising that every quadratic graph is a transformation of , and using this knowledge as an aid for sketching parabolas from their equations. Reasoning through explaining how different equivalent forms of an equation highlight different features of the corresponding graph. Considering different levels of student ability Level 8 Students who are working at this level could: Explore the relationship between simple quadratic sequences defined by tables of values with a constant second difference and the corresponding parabolic graphs. Level 10 Students who are working at this level could: Use graphical guess – check and refine method to identify a sequence of nested intervals containing a solution for equations of the form: quadratic = constant, quadratic = linear and quadratic = quadratic. Assessment ideas Students carry out an investigation where they explore possible equations of real world objects that can be modelled with a quadratic function, such as the arch of a bridge and the curve formed by a chain hanging between two posts. Resources AMSI NCTM Illuminations CIMT FUSE: Discover resources aligned to the Victorian Curriculum Notes