How do you identify the important parts of #y= x^2+2x# to graph it?

1 Answer
Oct 6, 2015

y:intercept: #0#
x-intercepts: #0# and #-2#
vertex at: #(-1,-1)#

Explanation:

The y-intercept is the value of #y# when #x=0#
#color(white)("XXX")y=0^2+2(0)=0#

The x-intercepts are the values of #x# when #y=0#
#color(white)("XXX")0=x^2+2x=(x)(x+2)#
#color(white)("XXX")x=0# or #x=-2#

Convert #y=x^2+2x# into vertex form:
#color(white)("XXX")y=(x^2+2x+1)-1#
#color(white)("XXX")y=(x+1)^2-1#
#color(white)("XXX")y=(x-(color(red)(-1)))^2+(color(blue)(-1))#
which is the vertex form of the equation with the vertex at #(color(red)((-1)),color(blue)((-1)))#