While searching to learn about complex numbers on the Internet, I was referred also to quadratic equations. Several graphic examples showed how "completing the square" uses a quadratic equation to calculate the length of sides of a square for a new desired area size, which I understood. I also saw examples of how graphing a quadratic equation creates a parabola, which I understood.
How can a quadratic equation represent a square with straight-line sides, AND a parabola with exponential curves? They seem completely different. In fact, I have not found one source, that mentions both in the same article. Is the link or relationship between them, because of the exponential term in the quadratic equation?
Best Answer
A parabola does not have any exponential curves. An exponential curve would be something like the graph of $y=10^x.$
A parabola has a polynomial curve with a shape similar to the graph of the formula $y=x^2,$ where $x^2$ is the area of a square of side $x$ — see the relationship to a square?