SOLUTION: how do you know if a parabola opens up or down?

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Question 1097586: how do you know if a parabola opens up or down?
Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You just look at the graph (since you know you have a parabola and are looking at it already) and either the vertex is at the bottom or it is at the top. If on the bottom, parabola opens UP. If vertex at the top then parabola opens DOWN. You just SEE it.




THIS IS WHAT YOU WANT:

If you have no given graph but do have an equation or the function, then
y=ax%5E2%2Bbx%2Bc
and if a%3C0, the parabola opens DOWNWARD.
If a%3E0, then parabola opens UPWARD.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A parabola that opens up or down has an equation of the form
y=a%2Ax%5E2%2Bb%2Ax%2Bc where a%3C%3E0%29 , b and c are real numbers.
If a%3E0 , as abs%28x%29 increases, ax%5E2%3E0 increases,
taking the graph up, up and away.
The terms bx and c could be pulling in the opposite direction,
but as x%5E2 increases faster than abs%28x%29 ,
eventually the ax%5E2 term will win.
The graph looks like a smiley face, or like a bowl with the opening pointing up.


If a%3C0 , ax%5E2%3C0 and going down as abs%28x%29 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.