Quadratic Inequalities

We may be given the curveandasked to find the set of values offorwhich

We can start by sketching the curve and obtain:

We can just read the solutions off here:

orWecould have factorised the

expression fortoobtainandsolvedtoobtainhencethe set of values of

For the quadratic above, since the coefficient ofis1 which is positive, we know it will be a “bum” curve,so the setof solutions forwillcome in two parts,or

The curve shown above isWeare asked for example to find the set of values offorwhichWecan see from the graph that there is only one set of values:Wecould have factorised the expression fortoobtainandsolvedtoobtainhencewe could write down the set of values of

The curve shown isWeare asked

to solveThecurve is a “breast” curve and we can read off the solutionsor

We can also factorise the expression fortoobtain andsolvehencefinding the set of solutions just given.