Question 741295
{{{x^2 -6x=5}}} 


A) Is the point ({{{-3}}},{{{32}}}) on the graph {{{f}}}?


{{{f(x)=x^2-6x-5}}} 

{{{32=(-3)^2-6(-3)-5}}} 

{{{32=9+18-5}}} 

{{{32<>22}}}.....so, the point ({{{-3}}},{{{32}}}) is {{{not}}} on the graph {{{f}}}

b)List the {{{y-intercepts}}} 

{{{f(x)=x^2-6x-5}}}....set {{{x=0}}}

{{{f(0)=0^2-6*0-5}}}

{{{f(0)=-5}}}.......the {{{y-intercept}}} is at ({{{0}}},{{{-5}}})




c)List the {{{x-intercepts}}}?

{{{f(x)=x^2-6x-5}}}....set {{{f(x)=0}}}

{{{0=x^2-6x-5}}}....solve for {{{x}}}


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


 {{{x = (-(-6) +- sqrt( (-6)^2-4*1*(-5) ))/(2*1) }}}


{{{x = (6 +- sqrt(36+20 ))/2 }}}


{{{x = (6 +- sqrt(56))/2 }}}


{{{x = (6 +- 7.48)/2 }}}

solutions:

{{{x = (6 + 7.48)/2 }}}

{{{x = 13.48/2 }}}

{{{x = 6.74 }}}

or

{{{x = (6 -7.48)/2 }}}

{{{x = -1.48/2 }}}

{{{x = -0.74 }}}


the {{{x-intercepts}}} are at ({{{6.74}}},{{{0}}}) and ({{{-0.74}}},{{{0}}})


d)What is the domain of f(x)?

all real numbers {{{x}}} in interval

({{{-infinity}}},{{{infinity}}})


{{{ graph( 600, 600, -10, 10, -20, 10, x^2-6x-5) }}}