Power Functions and Polynomial Functions · Exercise 68

Use the information about the graph of a polynomial function to determine the function. Assume the leading coefficient is 1 or –1. There may be more than one correct answer.

The $y-$ intercept is $\left(0,-4\right).$ The $x-$ intercepts are $\left(-2,0\right)$, $\left(2,0\right).$ Degree is 2.
End behavior: as $x\to -\infty$, $f\left(x\right)\to \infty$; as $x\to \infty$, $f\left(x\right)\to \infty .$

OpenStax, Algebra and Trigonometry 2e · §5.2 Power Functions and Polynomial Functions · Exercise 68