Question

Esmeralda and Heinz are working to graph a polynomial function, f(x). Esmeralda says that the third-degree polynomial has four intercepts. Heinz argues that the function only crosses the x-axis three times. Is there a way for them both to be correct? why?

Answer 1

There are only 3 intercepts at the most here. There could be less than 3 depending upon if some of the solutions are nonreal imaginary ones, but there can only be 3 at the most.

Answer 2

Because this is a cubed polynomial, there are only 3 solutions. A solution to a polynomial is defined by where the graph either crosses the line or has a point of inflection. Where it crosses the line is a real solution, where it has a point of inflection is a nonreal imaginary solution.

Answer 3

so it would be no, right? then i would just explain what you said?

Answer 4

It would be no, you are correct and then just explain what I said. That's right.

Answer 5

That second graph has 1 real solution and 2 imaginary. The real one is where it crosses the x axis, and the two imaginary are the "high point" at the top of the upwards curve, and the other imaginary is the "low point" at the bottom of the downwards curve.

Answer 6

thank you so much =)