While talking about different types of equations, a student in my class asked: Why we use the word quadratic to refer to second-degree equations?
Here is some context:
1) Linear ($x^1$) equations make sense, because the graph of a linear equation is a straight line.
2) Exponential ($a^x$) equations make sense, because $x$ is in the exponent, and my students will soon learn to recognize graphs of exponential equations.
3) Cubic ($x^3$) equations make sense, because $x$ is being cubed, and my students will soon learn to recognize graphs of cubic equations.
... so why do we use the word "quadratic" to refer to second degree equations? My students already know that the graph of a quadratic equation can be called a "parabola," and the word QUADratic sounds like it has something to do with the number four, rather than squaring.
Follow up question: Would it be better to call $x^2$ equations "parabolic" referring to the shape they make when graphed? Or why not call them "squared" equations in the same way we use for higher-degree equations?