Carefully and accurately sketch the polynomial. Be sure to label all zeroes, the y-intercept, and any minima or maxima. Use your graphing calculator to find the coordinates if any minima or maxima (round to two decimal places).

P(x)=-2x^4+x^3+6x^2=-x^2(x-2)(2x+3)

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frika

The graph of the polynomial function is represented in the attached diagram.

1) Zeroes:

P(x)=0 when

  • x=0;
  • x=2;
  • x=-3/2.

2) y-intercept:

when x=0, then

[tex]P(0)=-0^2(0-2)(2\cdot 0+3)=0.[/tex]

Thus, y-intercept is at point (0,0).

3) Minima and maxima points:

  • minima - (0,0);
  • maxima - (-1.05,3.03) and (1.43,6.83)
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