Precalculus : Graph a Parabola
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Example Question #1 : Parabolas
Which of the following could be the graph of f(x)?
Which of the following could be the graph of f(x)?
Begin by realizing this must be a downward facing parabola with its vertex at (0,3)
We know this because of the negative sign in front of the 5, and by the constant term of 3 on the end.
This narrows our options down to 2. One is much narrower than the other, although it may seem counterintuitive, the narrower one is what we need. This is because for every increase in x, we get a corresponding increase of times 5 in y. This translates to a graph that will get to higher values of y faster than a basic parabola. So, we need the graph below. to further confirm, try to find f(1)
So, the point (1,-2) must be on the graph, which means we must have:
Example Question #1 : Parabolas
Describe the orientation of a parabola with the following equation:
Facing up
Facing down
Facing to the left
None of the other options
Facing to the right
Facing down
The coefficient of the squared term tells us whether the parabola faces up or down. Parabolas in general, as in the parent function, are in the shape of a U. In the equation given, the coefficient of the squared term is 
Example Question #2 : Parabolas
Describe the orientation of the parabola below:
Facing right
Facing left
None of the other options
Facing down
Facing up
Facing up
The coefficient of the squared term tells us whether the parabola faces up or down. Parabolas in general, as in the parent function, are in the shape of a U. In the equation given, the coefficient of the squared term is 
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