Question

Please help for a medal and fan?!?!

Answer 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.

Answer 2

"third-degree polynomial has four intercepts"

that statement is somewhat true. If you change the statement to "third-degree polynomial has AT MOST four intercepts" then it would always be true.

consider the x and y intercepts

any polynomial will have exactly 1 y intercept
any third degree polynomial will have at most 3 x intercepts (but it might have 2 or 1 x intercept)

so any third degree polynomial has at most 1+3 = 4 intercepts total