Question 1089048
An {{{x}}}-intercept is the point where a parabola crosses the x-axis. This point is also known as a {{{zero}}}, {{{root}}}, or {{{solution}}}.

the expression {{{b^2 – 4ac}}}, called the "{{{discriminant}}}", and we can use it to find out what kind and how many roots the quadratic function have 

rule:

if {{{b^2 -4ac > 0}}}, Discriminant is greater than zero, Positive Discriminant:{{{Two}}}{{{ Real}}} Solutions

if {{{b^2-4ac = 0}}}, Discriminant is equal to zero. {{{One}}}{{{ Real}}} Solution

if {{{b^2 -4ac < 0}}}, Discriminant is less than zero ,Negative Discriminant: {{{No}}}{{{ Real}}} Solutions => means {{{no}}} {{{x}}}-intercepts


so, you will use {{{b^2 -4ac < 0}}} for {{{f(x)=ax^2-6x+3}}}

since {{{a=a}}}, {{{b=-6}}}, and {{{c=3}}}, you have

{{{(-6)^2 -4a*3< 0}}}
{{{36 -12a< 0}}}
{{{36 < 12a}}}
{{{36/12 < a}}}
{{{a>3}}}

check:

if {{{a>3}}}, we can use {{{a=4}}} and see the graph of {{{f(x)=4x^2-6x+3}}}

{{{ graph( 600, 600, -10, 10, -10, 10, 4x^2-6x+3) }}} 

as you can see, there is no x-intercept