SOLUTION: The degree of the polynomial function f(x) is 4. The roots of the equation f(x)=0 are −8 , −5 , 1, and 2. Which graph could be the graph of f(x) ? could someon

Algebra ->  Rational-functions -> SOLUTION: The degree of the polynomial function f(x) is 4. The roots of the equation f(x)=0 are −8 , −5 , 1, and 2. Which graph could be the graph of f(x) ? could someon      Log On


   

Question 1124258: The degree of the polynomial function f(x) is 4.
The roots of the equation f(x)=0 are −8 , −5 , 1, and 2.
Which graph could be the graph of f(x) ?
could someone show me how to grah this please
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39631) About Me  (Show Source):
You can put this solution on YOUR website!
The known degree tells you the basic shape and the basic ends behavior. The given roots tells you where the function crosses the x-axis.

You may be able to assume or choose a positive leading coefficient and the function can start as f%28x%29=%28x-2%29%28x-1%29%28x%2B5%29%28x%2B8%29. You can choose whatever constant factor you want, but NOT ZERO. The roots would be unaffected.

Since degree 4 is EVEN You expect unbound left and right to be Either both increasing; OR both decreasing.

You can use a graphing tool to find what the graph looks like if you want to avoid hand-drawing.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The graph of crosses the -axis at -8, -5, 1, and 2 and nowhere else. Any given graph with those characteristics is a candidate for your answer. Any graph that crosses the -axis at more than four places, less than 4 places, or at different places must be excluded.

In general, you cannot find the graph of because the function could be any of the infinite set of functions defined by:



Where


John

My calculator said it, I believe it, that settles it