What are the y- and x-intercepts for #f(x) = 2x^3 - 6x^2 - 20x#?

1 Answer
xurongna_ · Shwetank Mauria
Sep 17, 2017

#y# intercept at #(0,0)#
#x# intercepts at #(-2,0), (0,0), (5,0)#

Explanation:

graph{2x^3-6x^2-20x [-22.8, 22.81, -11.4, 11.4]}

The y-intercept is 0, because the function hasn't specified a y-intercept in. (if it did, it wouldn't have an x-coefficient)

For the x-intercepts, find where the y coordinate is 0. In this case, it's (-2,0), (0,0) and (5,0). These are also the solutions to the equation:
#0=2x^3 - 6x^2 - 20x#

As #2x^3-6x^2-20x=2x(x^2-3x-10)=2x(x-5)(x+2)#

and hence #f(x)=0# for #x=-2,0# and #5#.
Hope this helps.

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