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Determine the intercepts with the axes for the function y = x3 − 2x2 − 3x.

Mathematics

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Graph of y = x³ − 2x² − 3x

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Key points of y = x³ − 2x² − 3x
Pointxy
x-intercept−10
Maximum−0.540.88
x-intercept00
Minimum1.87−6.06
x-intercept30

The given function is y=x3−2x2−3xy = x^3 - 2x^2 - 3x.

9.1 Determine the intercepts with the axes.

Step 1: Find the y-intercept.
Set x=0x = 0 in the function:

y=(0)3−2(0)2−3(0)y = (0)^3 - 2(0)^2 - 3(0) y=0y = 0

The y-intercept is (0,0)\boxed{(0, 0)}.

Step 2: Find the x-intercepts.
Set y=0y = 0 in the function:

x3−2x2−3x=0x^3 - 2x^2 - 3x = 0

Factor out xx:

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