AC9M9A04
See also: Learning Areas / Mathematics / Mathematics / Algebra / Year 9
identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate
Elaborations
- AC9M9A04_E1 - recognising that in a table of values, if the second difference between consecutive values of the dependent variable is constant, then it is a quadratic
- AC9M9A04_E2 - graphing quadratic functions using digital tools and comparing what is the same and what is different between these different functions and their respective graphs; interpreting features of the graphs such as symmetry, turning point, maximum and minimum values, and determining when values of the quadratic function lie within a given range
- AC9M9A04_E3 - solving quadratic equations algebraically and comparing these to graphical solutions
- AC9M9A04_E4 - using graphs to determine the solutions of quadratic equations; recognising that the roots of a quadratic function correspond to the \(x\)-intercepts of its graph and that if the graph has no \(x\)-intercepts, then the corresponding equation has no real solutions
- AC9M9A04_E5 - relating horizontal axis intercepts of the graph of a quadratic function to the factorised form of its rule using the null factor law; for example, the graph of the function \(y=x^2-5x+6\) can be represented as \(y=(x-2)(x-3)\) with \(x\)-axis intercepts where either \((x-2)=0\) or \((x-3)=0\)
- AC9M9A04_E6 - recognising that the equation \(x^2=a\), where \(a>0\), has \(2\) solutions, \(x=\sqrt a\) and \(x=\)-\(\sqrt a\); for example, if \(x^2=39\) then \(x=\sqrt{39}=6.245\) correct to \(3\) decimal places, or \(x=\)-\(\sqrt{39}=\)-\(6.245\) correct to \(3\) decimal places, and representing these graphically
- AC9M9A04_E7 - graphing percentages of illumination of moon phases in relation to First Nations Australians’ understandings that describe the different phases of the moon
Achievement Standard Components
- ASMAT905 - Students use mathematical modelling to solve problems involving change in financial and other applied contexts, choosing to use linear and quadratic functions.
- ASMAT906 - They graph quadratic functions and solve monic quadratic equations with integer roots algebraically.