I was teaching this topic in sch the other day and as expected, students encountered quite a number of problems with this topic. Many of my tuition students over the years also reported the same problems in handling issues related to Quadratic Functions.
Some of these problems are:
(1) not understanding that alpha and beta by themselves also satisfy the quadratic eqn because they are the roots of the equation! So it’s not just abt finding the sum and product of roots;
(2) not knowing the condition for the discriminant (b^2 – 4ac) when the question involves the phrase “for which the function is never positive or never negative”;
(3) not being sure whether one is required to solve an inequality involving the discriminant or the function itself;
(4) not knowing how to complete the square to determine the maximum or minimum value of a quadratic function (even those who can do it do not understand why it works!);
(5) not recognising that “real and distinct roots”, “real and equal roots”, and “no real roots” have other names that express the same meaning.
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