Yasmin

2021-06-03

Is the following function a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.

$g(x)=3-\frac{{x}^{2}}{4}$

okomgcae

Skilled2021-06-04Added 93 answers

$g\left(x\right)=3-\frac{{x}^{2}}{4}\text{to}g\left(x\right)=-\frac{1}{4}{x}^{2}+3$.

This is a polynomial function.

The highest power of x is 2.

So, degree of the polynomial is 2.

The standard form of a polynomial function is,

$g(x)={a}_{2}{x}^{2}+{a}_{1}x+{a}_{0},\text{}where\text{}{a}_{2}=-\frac{1}{4},{a}_{1}=0\text{}and\text{}{a}_{0}=3$ $\Rightarrow g(x)=-\frac{1}{4}{x}^{2}+3$

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