College Algebra, Chapter 4, Chapter Review, Section Review, Problem 18

Graph the polynomial $P(x) = -2x^3 + 6x^2 - 2$ by using a graphing device. Find the $x$ and $y$ intercepts and the coordinates of all local extrema. Describe the end behavior of the polynomial.







Based from the graph, the $x$ intercepts can be approximated as $-0.5, 0.65$ and $2.95$. On the other hand, the value of the $y$ intercept is $2$. Also, the coordinate of the local maximum is $(2, 6)$. While the coordinate of the local minimum is $(0, -2)$. More over, the function has end behavior of $y \to - \infty$ as $x \to \infty$ and $y \to \infty$ as $x \to - \infty$.