Question 69894
Find the x intercepts
y = x^2 - 3x - 1 
:
The x intercepts occur when y = 0, (when a graph crosses the x axis)
:
x^2 - 3x - 1 = 0; solve for x, the solutions will be the x intercepts
:
This equation cannot be factored so you have to find x using the quadratic formula
In this equation a = 1 b = -3; c = -1
:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
{{{x = (-(-3) +- sqrt( -3^2- 4 * 1 * -1 ))/(2*1) }}}
:
{{{x = (+3 +- sqrt( 9 - (-4) ))/(2) }}}
:
{{{x = (+3 +- sqrt( 9 + 4 ))/(2) }}}
:
{{{x = (+3 +- sqrt( 13 ))/(2) }}}
:
{{{x = (+3 +- 3.6)/(2) }}}
:
2 solutions:
{{{x = (+3 + 3.6)/(2) }}}
{{{x = (+6.6)/(2) }}}
x = +3.3
and
{{{x = (+3 - 3.6)/(2) }}}
{{{x = (-.6)/(2) }}}
x = -.3
:
x = +3.3 and -.3; these are the x intercepts as illustrated in this graph:
{{{ graph( 300, 200, -3, 8, -8, 8, x^2 - 3x - 1) }}}
:
Notice that the graph "intercepts" the x axis at -.3 and + 3.3
:
Can you understand this now?