Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.
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medal and fan
Nope, a third degree polynomial will always only have 3 or less intercepts.
Not the answer you are looking for? Search for more explanations.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = x^3 − x^2 − 4x + 4
g(x) = x^3 + 2x^2 − 9x − 18
g(x) = x^3 − 3x^2 − 4x + 12
g(x) = x^3 + 2x^2 − 25x − 50
g(x) = 2x^3 + 14x^2 − 2x − 14
The first g(x), as x goes to infinity g(x) will be infinity. As x goes to negative infinity, g(x) will go to negative infinity. Y intercept would be 4.