Question 936660
Why does a quadratic equation have two answers?
y = ax^2 + bx + c
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
Actually, it doesn't always... 
only if  {{{sqrt( b^2-4*a*c )}}} > 0 does it have two 'real' answers... (Blue)
{{{sqrt( b^2-4*a*c )}}} = 0 , one answer. Ex: y = x^2 (Green)
{{{sqrt( b^2-4*a*c )}}} = 0, Imaginary roots only, does not cross x-axis (Purple)
...
x^2(green),(x-1)^2 -1(Blue), (x-1)^2 +3 (Purple)
graphically a quadratic equation is a Parabola:
generally, it will cross the x-axis twice...but not always...
{{{drawing(300,300, -10, 10, -10, 10,  grid(1),

graph( 300, 300,  -10, 10, -10, 10,0, x^2,(x-1)^2 -1, (x-1)^2 +3))}}}