Question

How do you graph `y=2x^2(x-2)^3(x+8)`?

Answer 1

See explanation.

Explanation:

Zeros of y are 0, 0, 2, 2, 2 and -8.

Zeros of y' are -7.55 0, 0.822, 2 and 2.

Zeros of y'': 2 and two more, giving points of inflexion.

The graph has x- intercepts ( y = 0): `-8, 0 and 2`.

Two differently scaled graphs reveal all these aspects.

graph{y-2x^2(x-2)^3(x+8)=0 [-20, 20, -90000,90000]}

graph{y-2x^2(x-2)^3(x+8)=0 [-20, 20, -100, 100]}