Sketch the curve with equation

y = (x -1)³ - 4(x - 1)

It's not really the sketching which is the problem but more working out where the graph crosses the x-axis and y-axis? I can see that it crosses the x-axis at 1 but am clueless as to the other two parts at which it crosses the x-axis .. thanks!

1 answer

well, try factoring it

y = (x-1)((x-1)^2 - 4)
= (x-1)(x-1+2)(x-1-2)
= (x-1)(x+1)(x-3)

That help?

Naturally, the y-intercept (at x=0) is at y=3
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