Question

Why can't the graphing calculator be used to solve (or approximate solutions to) all polynomial equations?

Answer 1

@Directrix @Nnesha @ArkGoLucky @dtan5457

Answer 2

To be honest, solving "by graphing" is an achingly trendy but somewhat bogus topic. The basic idea behind solving by graphing is that, since the "solutions" to "ax2 + bx + c = 0" are the x-intercepts of "y = ax2 + bx + c", you can look at the x-intercepts of the graph to find the solutions to the equation. There are difficulties with "solving" this way, though....

When you graph a straight line like "y = 2x + 3", you can find the x-intercept (to a certain degree of accuracy) by drawing a really neat axis system, plotting a couple points, grabbing your ruler and drawing a nice straight line, and reading the (approximate) answer from the graph with a fair degree of confidence.

On the other hand, a quadratic graphs as a wiggly parabola. If you plot a few non-x-intercept points and then draw a curvy line through them, how do you know if you got the x-intercepts even close to being correct? You don't. The only way you can be sure of your x-intercepts is to set the quadratic equal to zero and solve. But the whole point of this topic is that they don't want you to do the (exact) algebraic solving; they want you to guess from the pretty pictures.

So "solving by graphing" tends to be neither "solving" nor "graphing". That is, you don't actually graph anything, and you don't actually do any of the "solving". Instead, you are told to punch some buttons on your graphing calculator and look at the pretty picture, and then you're told which other buttons to hit so the software can compute the intercepts (or you're told to guess from the pretty picture in the book, hoping that the printer lined up the different print runs for the different ink colors exactly right). I think the educators are trying to "help" you "discover" the connection between x-intercepts and solutions, but the concept tends to get lost in all the button-pushing. Okay, enough of my ranting...

Answer 3

@GodGirl360

Answer 4

Thank you @ElonaSuschick

Answer 5

Anytime!!