Maths · Graphs of simple functions
Identify the graph of the polynomial function =x^{4}-2 x^{3}-x^{2}+2 x \)
Identify the graph of the polynomial function \( \boldsymbol{f} \) \( f(x)=x^{4}-2 x^{3}-x^{2}+2 x \)
- A. graph a
- B. graph b
- C. graph c
- D. graoh d
Step-by-step solution
The polynomial f(x)=x^4-2x^3-x^2+2x factors as x(x-1)(x-2)(x+1), giving roots at x=-1, 0, 1, 2. With a positive leading coefficient and even degree, the graph rises on both ends and crosses the x-axis at these four points. The sign pattern (positive for x<-1, negative for -1<x<0, positive for 0<x<1, negative for 1<x<2, positive for x>2) indicates three turning points. Among the options, graph a matches this behavior.
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