May 28th, 2015
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As you can see here, the parabola is open upwards and it will only have a minimaAs you can see here, the parabola is open downwards and it will only have a maximaThe nature of the graph of the quadratic equation is decided by the co-efficient of x^2.If the co-efficient of x^2 is greater than 0, the parabola will be open upwards and hence it will have a minima.If the co-efficient of x^2 is less than 0, the parabola will be open downwards and hence it will have a maxima.Once you have decided whether it will be a maxima or a minima the next task is to figure out two things:a) The point at which the maxima / minima occursb) The maximum / minimum value of the quadratic equationLet us try to figure these values out with the help of an example of both types i.e. when co-efficent of x^2 is greater than 0 and when it is less than 0Case 1: a > 0Now, we know that a perfect square is always non-negative=> The lowest value that (x-2)^2 can take is 0=>The minimum value that the entire quadratic can take is 3=>The minima occurs at x = 2 when x-2 is 0Case 2: a < 0Now, we know that a perfect square is always non-negative=> The lowest value that (x+3)^2 can take is 0=> The maximum value that the entire quadratic can take is 16=> The maxima occurs at x = -3 when x+3 is 0As you might have realised, the above idea of completing a square can be used to find out the maximum / minimum value and also the point at which the maxima/minima occurs in any quadratic equation

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