What is the x intercept of #yx= 6x^2/2 + 4x#?

1 Answer
Nov 1, 2015

x-intercepts: #x=0# and #x=-4/3#

Explanation:

The x-intercept is the value(s) of #x# when #y=0#

#yx=6x^2/2+4x#
when #y=0# is equivalent to
#3x^2+4x=0#

This factors as
#x(3x+4)=0#

with solutions
#x=0 and x=-4/3#

Alternate way of looking at it
#yx=6x^2+4x#
can be simplified by dividing by #x#
provided #color(black)(x!=0)#

In this case we would have the linear equation (graph below)
#y=3x+4#
(with the solution #x=-4/3# when #x!=0#)
graph{xy=3x^2+4x [-10, 10, -5, 5]}