Question #d9bde

1 Answer
Jul 19, 2017

Answer:

#(0, 0) " " and " " (-5/2, 0)#

Explanation:

The #x# intercept of a function occurs when #y=0#, since every point on the #x# axis has a #y# coordinate of #0#.

Therefore, to find the #x# intercept(s), we need to plug in #color(red)0# for #color(blue)y# and solve for #x#:

#color(blue)y = 2x^2 + 5x - 3color(blue)y#

#color(red)0 = 2x^2 + 5x - 3(color(red)0)#

#0 = 2x^2 + 5x#

Notice that you can factor out #x# from both terms:

#0 = (x)(2x+5)#

Remember that if #a xx b = 0#, then either #a=0# or #b=0#.

#x = 0 " " or " " 2x+5 = 0#

#x = 0 " " or " " 2x = -5#

#x = 0 " " or " " x = -5/2#

So the #x# intercepts are:

#(0, 0) " " and " " (-5/2, 0)#

Final Answer