Final answer:
To find the intercepts and axis of symmetry and vertex of a cubic function, set y = 0 to find the x-intercepts, set x = 0 to find the y-intercept, use x = -b/(2a) to find the axis of symmetry, and calculate the average of the x-intercepts to find the vertex.
Step-by-step explanation:
The equation y = -2x(x-1)(x+5) represents a cubic function. To find the x-intercepts, set y = 0 and solve for x. The x-intercepts or roots of the equation are the values of x where the function crosses the x-axis. To find the y-intercept, set x = 0 and solve for y. The y-intercept is the point where the function crosses the y-axis.
To find the axis of symmetry, use the formula x = -b/(2a), where a, b, and c are the coefficients of the quadratic term, linear term, and constant term, respectively. The axis of symmetry is a vertical line that passes through the vertex of the parabola.
The vertex of a cubic function can be found by using calculus or by finding the average of the x-intercepts.