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

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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) About Me  (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:
ax%5E2%2Bbx%2Bc+=+0
Look at the coefficient of the x%5E2 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) About Me  (Show Source):
You can put this solution on YOUR website!
If the leading coefficient is positive (for instance y=x%5E2) then you will have a parabola opening up like this:
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+x%5E2%29+

So in this case you will have a minimum


If the leading coefficient is negative (for instance y=-x%5E2) then you will have a parabola opening down like this:
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+-x%5E2%29+

So in this case you will have a maximum