Maths · Graphs of simple functions
Identify the graph of the polynomial function =x^{4}+x^{3}-2 x^{2} \) \begin{tab
Identify the graph of the polynomial function \( \boldsymbol{f} \) \( f(x)=x^{4}+x^{3}-2 x^{2} \) \begin{tabular}{|l|l|l|l|l|} \hline 1 & 1 & & & \\ \hline & & & & \\ \hline & & & & \\ \hline & & & & \\ \hline & & & & \\ \hline & & & & \\ \hline \end{tabular}
- A. graph a
- B. graph b
- C. graph c
- D. graph d
Step-by-step solution
The polynomial f(x)=x^4+x^3-2x^2 factors as x^2(x+2)(x-1), with zeros at x=0 (double root), x=-2, and x=1. The leading coefficient is positive, so as x→±∞, f(x)→+∞. The double root at x=0 means the graph touches the x-axis and turns around. The graph crosses the x-axis at x=-2 and x=1, and there is a local maximum at x=0 with f(0)=0. The end behavior and intercepts match typical graph b among the options.
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