ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: ally1784 on January 15, 2021, 01:55:04 am
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Hey guys, when solving quadratic inequalities, how do you know which signs to use?
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There are a few methods out there:
(using the first question as an example)
1. Draw a mini diagram. You can see that the coefficient of the x2 term will be positive, so the parabola is concave up. You can infer the x-intercepts from the factorised form and from your diagram determine the range of values that satisfies the inequality. In this example, we want the parts of the parabola that are below the x-axis, and as such we take the part in between ie. between -4 and 1/2.
2. Relate concavity and the inequality on a case by case basis:
concave up + less than = in between x-intercepts
concave up + greater than = -infinity to lower x-intercept, higher x-intercept to +infinity
concave down + less than = -infinity to lower x-intercept, higher x-intercept to +infinity
concave up + greater than = in between x-intercepts
I personally drew diagrams because they were quick and much more verifiable imo (I could visualise it better). There are more methods than what I've suggested, and it honestly doesn't matter which way you go about doing it as long as you have valid working and the correct answer :)
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Definitely agree with fun_jirachi. My go to method was always drawing out diagrams for non-linear inequalities since those are so easy to mess up.