Question 111874: Determine whether the graph of each parabola opens upward or downward.
y=-1/2x2+3
Are the ordered pairs x=-3 and 2 1/2 and y=3 and -10?
Answer by MathLover1(20849)   (Show Source):
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Determine whether the graph of each parabola opens upward or downward.
We know that:
quadratic function is
 ,
and its graph is a
If  , it opens 
If  , it opens 
your parabola is:
As you can see  , that means }; consequently, your parabola opens
Are the ordered pairs x=-3 and 2 1/2 and y=3 and -10?
ordered pairs ( ,  ) are : ( ,  ) and ( ,  )
evaluating our function for ( , )
.. multiply both sides by 
and for ( , )
multiply both sides by 
ordered pairs ( , ) and (, ) are not on the graph of the function
| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=6 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: -2.44948974278318, 2.44948974278318.
Here's your graph:
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