How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given #y=x^4+2x^2+1#?

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Answer 1 · 2017-01-01T16:49:20

#y_("intercept")=1#

No x-intercept.

Set #X=x^2# giving:

#y=X^2+2X+1#

#y=(X+1)^2#

#+-(X+1)=sqrt(y)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Determine x intercept")#

Set #y=0#

#-X-1=0 => x^2=-1#

#x=+-sqrt(-1)" "->" "x=+-i#

#color(green)("Thus there is no "x_("intercept"))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Determine y intercept")#

#y_("intercept")# occurs at #X=0#

#y=X^2+2X+1" "->" "y=0^2+2(0)+1 = 1#

#color(green)(y_("intercept")=1#
Tony B