Problema Solution
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.
Answer provided by our tutors
It is possible for them to be both correct.
We could have a 3rd degree polynomial which crosses the x-axis 3 times and the y-axis 1 time.
In that case, we will have a polynomial which will have 4 intercepts yet crosses the x-axis exactly 3 times.
For ex. such polynomial is y = x^3 - x^2 - 4x + 4
click here to see the graph