Solving quadratic equations is one of the most important multi-step techniques that must be done in mathematics. Variables often affect real-life factors in multiple instances, which can result in a model that is quadratic in form. Here’s an example: An auditorium seats 1200 people and has sold out every night with show tickets selling for $5 each. The manager estimates for a $1 price increase, 100 fewer people will buy tickets. How can he model his revenue based on his ticket price? revenue = (ticket sold) (price per ticket) let = price increase in dollars Pricce per ticket = 5+ x Ticket sold = 1200 -100x Based on this we can get an expression for revenue, which after expanding gives us: Reveneu = (1200-100x)(5+x) = 6000 + 700x -100x^2 We should recognize this equation as an upside-down parabola. The price where the x value is a maximum can be found by solving for the two roots and taking the x-value in the middle. The min/max of a parabola is always half-way between the roots! For this post please consider how quadratic equations are found in professions you may be considering and provide a 1 paragraph initial post. Applications in hobbies, side jobs, and other interests would be great as well! As usual, read the whole discussion and follow up at least once during the week. Remember, not all phenomena will be modeled well by a quadratic equation. The beauty of math is by learning a vast number of mathematical equations, we can model anything. Quadratics are not a one-size-fits-all solution.
