AC9M9A04 Year 9 Mathematics

Content descriptor 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

• • Elaboration 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
• • Elaboration 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
• • Elaboration solving quadratic equations algebraically and comparing these to graphical solutions
• • Elaboration 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
• • Elaboration 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
• • Elaboration 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
• • Elaboration graphing percentages of illumination of moon phases in relation to First Nations Australians’ understandings that describe the different phases of the moon