SOLUTION: 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?

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): You can put this solution on YOUR website!

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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