Question 153941
The function is {{{y=x^2-8x+2}}}
To find the y-intercept, let x =0, so {{{y =0^2-8*0+2=2}}}
Thus the y-intercept is 2.
To find the x-intercept, let y=0, and determine the corresponding values of x by solving the following quadratic equation.
{{{x^2-8x+2=0}}}
Substitute
a = 1
b=-8
c=2
into the quadratic formula below
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
So
{{{x = (-(-8) +- sqrt( (-8)^2-4*1*2 ))/(2*1) }}}
{{{x = (8 +- sqrt( 64-8 ))/(2) }}}
{{{x = (8 +- sqrt( 56 ))/(2) }}}
{{{x = (8 +- sqrt( 14*4 ))/(2) }}}
{{{x = (8 +- 2sqrt( 14 ))/(2) }}}
{{{x = 4 +- sqrt( 14 )}}}
So the x-intercepts are {{{4+sqrt(14)}}} and {{{4-sqrt(14)}}}
{{{graph(300,300,-10,10,-10,10,x^2-8x+2)}}}