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Write one or two paragraphs on it. Express your vision of the topic in your own words.

How does quadratic function help us solve maximum/minimum problems?

Solution

Before getting into the details of the discussion ,we need to understand as to what is a maximum/minimum problem and how is it related to quadratic functions. A maximum /minumum problem or maxmin as it is generally called is a problem which deals with finding the maximum or the minimum value or both for a given condition which can be expresssed decisively in a mathematical expresssion. These are also called as optimization problems. the maxmin problems make use of the fact that the maximum or the minimum of an expression will be at that point of the expression where the curve defining the expression changes its direction from posive to negetive or vice versa. Clearly this takes place at the ebb of the curve defined by the expression given. The ebb (or the point of maxmin) is defined by the quadratic expression -b/2a where b is the coefficient of variable of first order and a is the coeffficent of variable of second order in the quadratic expression being taken .(y=ax²+bx+c)

While dealing with maxmin problems of quadratic nature, we generally break the expression into its vertex form (y=a(h-x)²+k ) so that it becomes easires to idenitfy the vertex cordinates(h,k) .

The quadratic function has a great impact on giving direction of solution in any maxmin problem . It lets us know of the points of maxima aor minima under a given condition . For eg., Engineers use quadratic functions to determine the maximum height or the minimum clearance under the support of the bridge at a variety of points. an architect can use it to design a structure with maximum area in a given land plot .Industries use the application of quadratic function in maxmin applications to measuretheir performance output and it helps them to optimize their performance.Thus application of quadratic function in maxmin expressions give a clear insight into the optimized values under given boundary conditions.