Question

the polynomial function ( f(x) ) is graphed below. fill in the form below regarding the features of this graph.

answer attempt 1 out of 2

the degree of ( f(x) ) is (\boxed{quad}) and the leading coefficient is (\boxed{quad}). there are (\boxed{quad}) different real zeros and (\boxed{quad}) relative extremes.

Explanation:

Step1: Identify polynomial degree

The graph has 2 turning points. For polynomials, degree $n$ has at most $n-1$ turning points. So $n-1=2 \implies n=4$.

Step2: Determine leading coefficient

As $x\to\pm\infty$, $f(x)\to+\infty$. For even-degree polynomials, this means leading coefficient $>0$.

Step3: Count real zeros

The graph crosses the $x$-axis at 2 distinct points, so 2 real zeros.

Step4: Count relative extremes

The graph has 2 "peaks/valleys" (turning points), so 2 relative extremes.

Answer:

The degree of $f(x)$ is $\boldsymbol{4}$ and the leading coefficient is $\boldsymbol{positive}$. There are $\boldsymbol{2}$ different real zeros and $\boldsymbol{2}$ relative extremes.