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The question is based on the false assumption that the quadratic formula is not used in daily life. Wrong, it IS!
Graphs in real life are used in at times when analysis of information is needed. for example, when tracking population growth of a species over a period of years scientists will use empirical data and field study to graph out how the species is growing or declining for study.
People use line graphs in businesses, and to compare data. Line graphs are mostly used when people are entrepreneurs. They figure out profit this way. Line graphs are also used when a product is made. They decide if they should continue to make this product, by how well the product sells. Line graphs show the change.
Scatter graphs. Line graphs may be used at a later stage when there is a better idea of the general shape of the line - whether it is a straight line, a quadratic curve, a logarithmic or exponential curve etc, or one of the standard probability distributions.