Determine a window that will provide a comprehensive graph of the polynomial function.
-$$y = 2 x ^ { 4 } + 2 x ^ { 3 } - 4 x ^ { 2 } - 3 x - 6$$
A) $[ - 2,2 ]$ by $[ - 10 , - 5 ]$
B) $[ - 3,3 ]$ by $[ - 10,5 ]$
C) $[ - 5,5 ]$ by $[ - 5,5 ]$
D) $[ - 10,10 ]$ by $[ - 8,8 ]$

Question

Quizplus · Accepted Answer

To graph a polynomial function comprehensively, the window must be wide enough to capture the significant turns and wide enough in the y-axis to capture the maximum and minimum points. Given the degree and coefficients of the polynomial $y = 2x^4 + 2x^3 - 4x^2 - 3x - 6$, a window of $[-3,3]$ by $[-10,5]$ is likely to encompass the critical points and the overall shape of the graph, considering the behavior of quartic functions and their potential for multiple turning points.

Determine a Window That Will Provide a Comprehensive Graph of the Polynomial