Which of the following graphs could represent a quartic function?

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Question:

Which of the following graphs could represent a quartic function?

Answer:

Answer:

D. Graph D

Step-by-step explanation:

As we know,

Quartic function is a function of the form , where a≠0.

That is, a quartic function is a polynomial of degree 4 called a quartic polynomial.

By the ‘Fundamental Theorem of algebra’, we have, ‘An n-degree polynomial will have ‘n’ number of real roots’.

Thus, we get,

A quartic polynomial will have 4 real roots and so, a quartic function has 4 zeros.

Since, a quartic function has 4 zeros. Its graph will cut the y-axis at 4 points.

Moreover, when a graph touches the axis, it is known to be a repeated zero.

So, from the options, we get,

Option D represents a quartic function as one of its root is repeated and it cuts the the graph 4 times.

From the answer and question examples above, hopefully, they can definitely guide the student resolve the question they had been looking for and keep in mind of each and every thing declared in the answer above. You may then have a discussion with your classmate and continue the school learning by studying the problem alongside one another.

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