Question 354042
To find x intercepts you set the equation equal to zero and solve for x.
{{{ f(x) = x^2-20x-800 }}} factor the equation
{{{ f(x) = (x-40)(x+20) }}} 
{{{ 0 = x-40 }}} add 40 to each side
{{{ x = 40 }}} 
{{{ 0 = x+20 }}} subtract 20 from each side
{{{ x=-20 }}}
So the x intercepts are (40,0) and (-20,0).
To find the y intercept you plug in x=0 into the equation and solve for y.
{{{ y = x^2-20x-800 = 0-0-800=-800 }}} So the y intercept is (0, -800). 
To find the x coordinate of the vertex you use the formula {{{ h = -b / (2a) = 20/2=10 }}} Then to find the y coordinate of the vertex, you plug in 10 into the equation and solve for y.
{{{ x^2-20x-800  = 10^2-20*10-800 = 100-200-800 = -900 }}} So the vertex is at (10,-900). 

Plot x and y intercepts and the vertex and smoothly connect the dots.

{{{ graph( 300, 300, -40, 60, -1000, 1000, x^2-20x-800 ) }}}