Question 799088
The standard form of a parabola's equation is generally expressed:

    {{{y = ax^2 + bx + c}}}
        The role of '{{{a}}}'
            if {{{a> 0}}}, the parabola opens {{{upwards}}}
            if {{{a< 0}}}, it opens {{{downwards}}}
        The axis of symmetry is the line {{{x = -b/2a }}}

given:

{{{f(x)=x^2-8x-6}}}...=>{{{f(x)=y}}}, {{{a=1}}},{{{b=-8}}}, and {{{c=-6}}}

so, since {{{a=1}}} =>{{{a> 0}}}, the parabola opens {{{upwards}}}

The axis of symmetry is the line {{{x = -b/2a }}}

{{{x = -(-8)/2*1 }}}

{{{x =8/2 }}}

{{{x =4 }}}

The vertex form of a parabola's equation is generally expressed as :

{{{y= a(x-h)^2+k}}}

    ({{{h}}},{{{k}}}) is the {{{vertex}}}

{{{f(x)=(x^2-8x+_)-6}}}..complete square

{{{f(x)=(x^2-8x+4^2)-6}}}

{{{f(x)=(x-4)^2-16-6}}} 


{{{f(x)=(x-4)^2-22}}}....=> {{{h=4}}} and {{{k=-22}}}

so, ({{{4}}},{{{-22}}}) is the {{{vertex}}}


 the {{{x}}} intercept: set {{{f(x)=0}}} and solve for {{{x}}}

{{{0=x^2-8x-6}}}.........use quadratic formula

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

 {{{x = (-(-8) +- sqrt( (-8)^2-4*1*(-6) ))/(2*1) }}} 

{{{x = (8 +- sqrt( 64+24 ))/2 }}} 

{{{x = (8 +- sqrt( 88))/2 }}} 

{{{x = (8 +- 9.38)/2 }}} 

solutions:

{{{x = (8 + 9.38)/2 }}} 

{{{x = 17.38/2 }}} 

{{{x = 8.69 }}} 

or

{{{x = (8 - 9.38)/2 }}} 

{{{x = -1.38/2 }}} 

{{{x = -0.69 }}} 

so, the {{{x}}} intercepts are ({{{8.69}}},{{{0}}}) and ({{{-0.69}}},{{{0}}})


{{{drawing(600,600,   -5, 15, -25, 10,   blue(line(4,10,4,-25))  , grid(0),
graph( 600,600,   -5, 15, -25, 10,  x^2-8x-6))}}}