Question 1097586
A parabola that opens up or down has an equation of the form
{{{y=a*x^2+b*x+c}}}  where {{{a<>0)}}} , {{{b}}} and {{{c}}} are real numbers.
If {{{a>0}}} , as {{{abs(x)}}} increases, {{{ax^2>0}}} increases,
taking the graph up, up and away.
The terms {{{bx}}} and {{{c}}} could be pulling in the opposite direction,
but as {{{x^2}}} increases faster than {{{abs(x)}}} ,
eventually the {{{ax^2}}} term will win.
The graph looks like a smiley face, or like a bowl with the opening pointing up.
{{{drawing(300,300,-0.9,0.9,-0.9,0.9,
locate(0.2,0.8,y=x^2),
graph(300,300,-0.9,0.9,-0.9,0.9,x^2))}}}
 
If {{{a<0}}} , {{{ax^2<0}}} and going down as {{{abs(x)}}} increases.
no matter what the values of {{{b}}} and {{{c}}} are, 
{{{y}}} will eventualy be negative and decreasing,
so the graph  goes down to the left and the right,
like a frown or an umbrella, and we say it opens down.
{{{drawing(300,300,-0.9,0.9,-0.9,0.9,
locate(0.2,0.8,y=-x^2),
graph(300,300,-0.9,0.9,-0.9,0.9,-x^2))}}}