AC9M9A04

Elaborations

• AC9M9A04_E1recognising 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_E2graphing 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_E3solving quadratic equations algebraically and comparing these to graphical solutions
• AC9M9A04_E4using 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_E5relating 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_E6recognising that the equation x^2=a, where a>0, has 2 solutions, x=√(a) and x=-√(a); for example, if x^2=39 then x=√(39)=6.245 correct to 3 decimal places, or x=-√(39)=-6.245 correct to 3 decimal places, and representing these graphically
• AC9M9A04_E7graphing percentages of illumination of moon phases in relation to First Nations Australians’ understandings that describe the different phases of the moon