Question 1204304
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The polynomial equation is of the form<br>
{{{p(x)=a(x+4)(x+1)(x-2)^2}}}<br>
The degree of the polynomial is 4, so the end behavior is the same both to the left and to the right.  If the leading coefficient a is positive, the end behavior in both directions is upward; if it is negative, the end behavior in both directions is downward.<br>
Assume that the leading coefficient is positive.  Then we have...<br>
end behavior upward to the left;
a single root at x=-4, so the graph crosses the x-axis, making the function value negative;
a single root at x=-1, so the graph crosses the x-axis, making the function value positive;
a double root at x=2, so the graph just touches the x-axis, after which the function value remains positive; and
end behavior upward to the right.<br>
A graph showing that behavior, using a leading coefficient of a=1:<br>
{{{graph(400,400,-5,5,-100,100,(x+4)(x+1)(x-2)^2)}}}<br>