Question

Your classmate Linus encounters difficulties in showing a sketch of the graph of y=2x^3 + 3x^2 - 4x - 6. You know that the quickest technique is the Leading Coefficient Test. You want to help Linus in his problem. What hint/clue should you give​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

The Leading Coefficient Test is a quick way to determine the end behavior of a polynomial function and thus sketch its graph. To use this method, one must look at the coefficient of the highest degree term (in this case, 2x^3) and determine whether it is positive or negative. If the coefficient is positive, the end behavior of the graph will be upwards, and if the coefficient is negative, the end behavior of the graph will be downwards.

Additionally, to help Linus with his problem, you can also explain to him how the degree of the polynomial affects the graph. The degree of a polynomial determines the number of turns or peaks that the graph will have. In this case, the degree of the polynomial is 3, which means the graph will have two peaks (or two valleys) and one inflection point.

With this information in mind, Linus can use the Leading Coefficient Test to determine the end behavior of the graph and use the degree of the polynomial to determine the general shape of the graph. Then, he can use critical points and intercepts to refine his sketch.

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