Question

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)

Answer 1

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

$P(0)=-0^2(0-2)(2\cdot 0+3)=0.$

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)