Final answer:
The polynomial –7 + 5m^4 + 9m - 3m^2 is of fourth degree because 5m^4 is the term with the highest exponent. Therefore, the polynomial is classified as quartic, not quadratic.
Step-by-step explanation:
To classify the given polynomial –7 + 5m^4 + 9m - 3m^2 by its degree, we first need to understand that the degree of a polynomial is the highest exponent of the variable in the polynomial, which in this case is m. Here, the term with the highest exponent is 5m^4, meaning that the degree of this polynomial is four. Therefore, the correct classification of the polynomial based on its degree is quartic.
Quadratic equations or functions, also known as second-order polynomials, have a degree of two, which means the highest exponent of the variable is two. This is not the case for our polynomial. Furthermore, Equation Grapher tools allow students to learn about graphing polynomials, and they can visually see how the degree of a polynomial affects its curve. In summary, the polynomial in question would produce a quartic curve if graphed.