Needed help with this math question.

Question

f(x)= 5x^2 - 3x + 4

Does f(x) represent a polynomial function? If so what's it's degree and type?

Answer 1

yeah, the function you listed represents a polynomial function! more specifically, since the highest exponent of a variable here is "2" that means that degree = 2 and this is a quadratic function :)

Answer 2

Any function consisting of one or more terms of variables with whole number exponents is a polynomial function. If it is in one variable (usually x), it is in the following form:

     ƒ(x) = a_nxⁿ + a_n-1x^n-1 + ... + a₁x + a₀ , 

   where a_n≠0 and, as stated earlier, all the exponents are whole numbers. 

The degree of the polynomial function is the value of the greatest exponent (i.e., this is an n^th degree polynomial since n is the greatest exponent).

     ƒ(x) = 5x² - 3x + 4

Since the value of the highest exponent in this polynomial is 2, then this is a 2^nd degree polynomial function. Such functions are known as quadratic functions and are graphically represented by a parabola.