Question 830937
{{{2x^2 - 8x + 10=y}}}

the {{{x-intercept}}} is a point with coordinates ({{{x}}},{{{ 0 }}})

so, set {{{y=0}}} and solve for {{{x}}}

{{{2x^2 - 8x + 10=0}}}

 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

 {{{x = (-(-8) +- sqrt( (-8)^2-4*2*10 ))/(2*2) }}}


{{{x = (8 +- sqrt( 64-80 ))/4 }}}

{{{x = (8 +- sqrt( -16 ))/4 }}}

{{{x = (8 +- 4i)/4 }}}

solutions:

{{{x = (8 + 4i)/4 }}}

{{{x = 8/4 + 4i/4 }}}

{{{x = 2 + i }}}


{{{x = (8 - 4i)/4 }}}

{{{x = 8/4 - 4i/4 }}}

{{{x = 2- i }}}

as you can see, {{{x = 2 + i }}} and {{{x = 2- i }}} are complex solutions; so, there is {{{NO}}} x-intercept



the {{{y-intercept}}} is a point with coordinates ({{{ 0 }}},{{{ y }}})

 and to find y-intercept, set {{{x=0}}} 

{{{2x^2 - 8x + 10=y}}}

{{{2*0^2 - 8*0 + 10=y}}}

{{{ 10=y}}}

so, the {{{x-intercept}}} is at a point ({{{0}}},{{{ 10 }}})


let's check it on a graph:

{{{ graph( 600, 600, -10, 10, -15, 15, 2x^2 - 8x + 10) }}}