SOLUTION: How can you tell from the equation of a parabola whether the graph has a maximum or a minimum value at its vertex?

Question 89183: How can you tell from the equation of a parabola whether the graph has a maximum or a minimum value at its vertex?

Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
You can tell in the following way!
The general form of the equation of a parabola is:

Look at the coefficient of the term, that's the a, and...
If a > 0 (positive), then the parabola opens upward and the graph has a minimum at its vertex.
If a < 0 (negative), then the parabola opens downward and the graph has a maximum at its vertex.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If the leading coefficient is positive (for instance ) then you will have a parabola opening up like this:

So in this case you will have a minimum

If the leading coefficient is negative (for instance ) then you will have a parabola opening down like this:

So in this case you will have a maximum
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