how to graph the polynomial function
f(x)= -x^4 - 4x^2 by hand. Please Help!!!
make it easy f(x)=-x^2(x^2+4)
it has a root at zero. It is at x=-infinity very negative. It crosses the axis,or touches it at x=0. At +inf, it is again very negative. Since it starts and ends in the negative, it cannot cross the y axis, so it touches it at x=0
Now, look at the near x behaviour.
let x=-1 then y=-1-4=-5
let x=1 then y=-1-5
one more point:
x=-3 y=-9(9-4)=-45
x=+3 y=-9(9-4)=-45
that is enough to sketch the graph. If you are not sketching, but graphing, you have to decide what region. Infinity is a very difficult point to plot.