High School

What are the x-intercepts of the graph \(y = -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108\)?

Answer :

Final answer:

The x-intercepts of the given graph can be obtained by setting the equation equal to zero and solving for x.

Explanation:

The x-intercepts of a graph represent the points where the graph intersects the x-axis. To find the x-intercepts of the given graph, set the equation equal to zero and solve for x. In this case, the equation is y = -x⁶ - 6x⁵ + 50x³ + 45x² - 108x - 108. Set y = 0 and solve for x:

-x⁶ - 6x⁵ + 50x³ + 45x² - 108x - 108 = 0

There is no simple algebraic way to obtain the solutions for this equation. However, you can use numerical methods or a graphing calculator to approximate the x-intercepts.

The x-intercepts of the graph are the values of x where the graph crosses or touches the x-axis.