document.write( "Question 533162: graph the function
\n" ); document.write( " f(x)= -2x^4-x^3+3x^2 \n" ); document.write( "

Algebra.Com's Answer #350984 by lwsshak3(11628) $\"\"$ $\"About$

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graph the function
\n" ); document.write( "f(x)= -2x^4-x^3+3x^2
\n" ); document.write( "f(x)= (-x^2)(2x^2+x-3)
\n" ); document.write( "0=(-x^2)(2x^2+x-3)
\n" ); document.write( "(-x^2)(2x+3)(x-1)=0
\n" ); document.write( "zeros: -3/2, 0, and 1
\n" ); document.write( "number line:
\n" ); document.write( "<....-....-3/2.....+.....0.....+.....1....-.....>
\n" ); document.write( "By inspection, when x>1, it can be seen that f(x)<1. Moving to the left, sign of the intervals switch if we go thru a zero of odd multiple like 1, 3, 5, etc. Interval signs do not switch when going thru zeros of even multiples like 2, 4, 6, etc. 1 and -3/2 are zeros of multiplicity 1, whereas, 0 is of multiplicity 2. Use signs of the intervals to help you draw the graph.
\n" ); document.write( "see graph below as a visual aid to draw the graph:
\n" ); document.write( "..
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+-2x%5E4-x%5E3%2B3x%5E2%29+\"$ \n" ); document.write( "

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