Question 718326
The x-intercepts of {{{y = x^2-40x-500}}} are where the graph intersects the x-axis. Since all points on the x-axis have a y-coordinate of 0, x-intercepts are found by replacing the y with zero and solving for x:
{{{0 = x^2-40x-500}}}
This factors fairly easily:
{{{0 = (x-50)(x+10)}}}
From the Zero Product Property:
x-50 = 0 or x+10 = 0
Solving these we get:
x = 50 or x = -10
The x-intercepts of {{{y = x^2-40x-500}}} are (50, 0) and (-10, 0).<br>
P.S. You get the same answers if you use the Quadratic Formula (or any other legitimate way) to solve {{{0 = x^2-40x-500}}}). I don't know how you came up with decimal answers. But if you used the Quadratic Formula, then you must have made a mistake somewhere (which is an argument for solving by factoring when possible). Here's the solution using the formula:
{{{x = (-(-40) +- sqrt((-40)^2-4(1)(-500)))/2(1)}}}
Simplifying...
{{{x = (-(-40) +- sqrt(1600-4(1)(-500)))/2(1)}}}
{{{x = (-(-40) +- sqrt(1600+2000))/2(1)}}}
{{{x = (-(-40) +- sqrt(3600))/2(1)}}}
{{{x = (-(-40) +-  60)/2(1)}}}
{{{x = (40 +-  60)/2}}}
which is short for:
{{{x = (40 +  60)/2}}} or {{{x = (40 -  60)/2}}}
Simplifying...
{{{x = 100/2}}} or {{{x = -20/2}}}
x = 50 or x = -10