Question

1. 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? Explain your answer.
@ganeshie8 @Luigi0210 @confluxepic @sleepyjess

Answer 1

@iGreen.

Answer 2

Hint : A \(n\)-degree polynomial can have atmost \(n\) x intercepts

Answer 3

okay so both of them can be correct?

Answer 4

Hmmmmm I just noticed something. " third-degree polynomial has four intercepts.", this just says intercepts, not x intercepts

Answer 5

But I would go with they mean x intercepts :)

Answer 6

Ahh good observation :) so they might include both x and y intercepts ?

Answer 7

im not sure anymore haha

Answer 8

That is what I was thinking, if so, then they would both be correct

Answer 9

neither am I lol

Answer 10

...

Answer 11

okay so can you explain how?

Answer 12

Well, a 3rd degree polynomial has 3 x intercepts, but Esmeralda says 4 intercepts. A function must cross the y axis unless it is a vertical line, which we know from the fact that it has 3 x intercepts that it isn't a vertical line.

Answer 13

so one is wrong and one is right and that explains it^

Answer 14

that explains both could be correct : 3 x intercepts + 1 y intercept = 4 intercepts

Answer 15

No, because it only crosses the x-axis 3 times because it has 3 roots, but it also has a y-intercept giving it 4 intercepts

Answer 16

okay. thanks

Answer 17

Heinz can also be correct becase a third-degree polynomial can have 3 x intercepts

Answer 18

And if you get it wrong, you can definitely challenge it.