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As mentioned in the previous lesson, trinomial quadratics containing a first degree and second degree term, along with a constant, are called complete quadratics. Just like pure and incomplete quadratics, solving complete quadratics is as simple as setting y = 0 and solving for x. Remember, to solve an equation means to find the values of…
So far in this unit, you have learned a variety of methods for solving quadratic equations: graphing, factoring, completing the square, and the quadratic formula. In this final section, you will learn how to apply these skills to solve problems related to situations that can be modelled by quadratic relations,…
Of the several methods we have for solving quadratics, the most useful is the quadratic formula. It will work for any quadratic, regardless of the type of roots, and it can easily be programmed into your calculator. Interestingly, the quadratic formula is derived by completing the square of the general form…
Arguably, the whole purpose behind learning how to factor quadratics and find its roots (also known as zeros) is to know how to sketch parabolas accurately. As you have come realize, many quadratic relations of the form y = ax² + bx + c can be factored to find the…
To solve a quadratic equation means to find values for x that make the y side of the equation equal to zero. Recall that a quadratic has a highest degree of 2. Generally, the highest degree in any equation dictates the maximum possible number of solutions. Thus a quadratic equation, being…
All quadratic equations have at least one minimum or maximum value. Think of a parabola, they either open upwards like a smile ∪ or face downwards like a frown ∩. What dictates the direction of opening is the a term. If the a term is positive, it open upwards (a minimum). If the…