SOLUTION: Good moprning everyone, This is my question: How do you graph a parabola. How do you know if the parabola opens upward or downward. Thank you Gina

Question 460473: Good moprning everyone,
This is my question:
How do you graph a parabola. How do you know if the parabola opens upward or downward.
Thank you
Gina
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The 1st step would be to find the axis of symmetry.
This would be a vertical line, . The parabola
is symmetrical to the left and right of this line.
If the equation is expressed as , then
.
The base, or the point with zero slope, will be .
Plug the value of back into the equation to get
If is positive, the parabola opens up.
If is negative, it opens down.
-----------------------------
Here's an example:

is negative, so it opens down.

is the axis of symmetry
Plugging this back in:

So, the base point is (3/4, -11)
The parabola can touch the x-axis in
1 point, 2 points, or no points.
Here's a plot:

The y-intercept is at , so

, so you have the point (0, -12)
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