Question 1045902

{{{y=-2x^2+12x-19}}}
to get y-intercept, set {{{x=0}}}

{{{y=-2*0^2+12*0-19}}}

{{{y=-19}}}

y-intercept is ({{{0}}},{{{-19}}})

to find x-intercepts set {{{y=0}}}

{{{0=-2x^2+12x-19}}}...both sides multiply by -1

{{{0=2x^2-12x+19}}}.........use quadratic formula


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}....in your case {{{a=2}}}, {{{b=-12}}}, and {{{c=19}}}


{{{x = (-(-12) +- sqrt( (-12)^2-4*2*19 ))/(2*2) }}}


{{{x = (12 +- sqrt( 144-152 ))/4 }}}


{{{x = (12 +- sqrt( -8 ))/4 }}}


{{{x = (12 +- sqrt( -1*4*2 ))/4 }}}


{{{x = (12 +- 2i*sqrt( 2 ))/4 }}}


{{{x = (cross(12)3/cross(4) +- cross(2)i*sqrt( 2 )/cross(4)2) }}}


{{{x = (3 +- i*sqrt( 2 )/2) }}}


complex solutions:

{{{x = 3 + i*sqrt( 2 )/2 }}}

{{{x = 3 - i*sqrt( 2 )/2 }}}