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Question 1204304: Write an equation and sketch an example of a quartic function with the zeros at - 4, - 1, 2 (order 2). Be sure to include an image of your solution.
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! NOT LIKE THAT. You want quadratic function with zero -4 and -1, with order 2. OF COURSE it is order 2, because QUADRATIC function.
Your description specifies "quadratic" function.
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You can do your own sketch. Lead coefficient can be either positive or negative. You pick! The simple example I gave would be
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Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
The polynomial equation is of the form
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.
Assume that the leading coefficient is positive. Then we have...
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.
A graph showing that behavior, using a leading coefficient of a=1:
Answer by ikleyn(52777)  (Show Source):
You can put this solution on YOUR website! .
Ignore the post by @josgarithmetic, since it is INCORRECT and IRRELEVANT.
His post demonstrates that he does not know / (does not understand) the term " quartic equation "
and mistakenly interprets it as " quadratic equation ".
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