Question 533162: graph the function
f(x)= -2x^4-x^3+3x^2
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! graph the function
f(x)= -2x^4-x^3+3x^2
f(x)= (-x^2)(2x^2+x-3)
0=(-x^2)(2x^2+x-3)
(-x^2)(2x+3)(x-1)=0
zeros: -3/2, 0, and 1
number line:
<....-....-3/2.....+.....0.....+.....1....-.....>
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.
see graph below as a visual aid to draw the graph:
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