A SIMPLE Way To Determine the Equation of a Polynomial Function From Its Graph (Degree 4 Example!)

[@MathByThePixel]

Get better at math with my epic weekly math tips and tricks ► math-by-the-pixel.ck.page/b963475226

[@kawaii80yo]

I was confused for a second for putting 1 as a, which is what I did, but turns out I was right

[@MathByThePixel]

I was genuinely surprised when it worked out that way myself! I promise it like never is 1 🤣

[@yajaman]

I think calling changing f(x) to y a 'notation swap' is missing the point of what a function is. A graph is a set of points. To plot the set of points of a function of one variable, you need two dimensions, one to plot the variable and one to plot the output. We plot the variable on the x axis, and the result on the y axis. So the y coordinate of the point is a *function* of the x coordinate. For a given point, you are plotting (x, f(x)) on the graph. So calling changing f(x) to y a notation swap is not really correct. f(x) is the very definition of the y coordinate of any point.

[@MathByThePixel]

f(x) is the notation we use to communicate the value of the function at the corresponding x-value. In the example in this video, we are working with x and y, and the graph has y depending on x. The point I was making was that we can interchange the two when substituting a point into our equation since we know our points are of the form (x, f(x)), or (x, y). I would consider this to be a matter of notation.