How do you understand Maximum and minimum. It says " if the parabola opens up/down..." what is the parabola and how does that determine max or min?

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How do you understand Maximum and minimum. It says " if the parabola opens up/down..." what is the parabola and how does that determine max or min?

Mathematics
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Which math class are you taking at the momen?
college algebra
For a parabola, If opening in the Y direction up/down, will have a max/min value at the vertex.

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If it opens up for example, the min value will be the vertex, and the max will be infinity.
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If it opens down the other way, the vertex would be the Maximum, and the minimum would be negative infinity. Do you have a specific example?
okay the problem I just did was a vertex (6,-2) which is maximum,-2. I completely guessed on it but its right. what I don't understand how to determine if its max or min based on the information given. My complete function was f(x)=-x^2+12-38, vertex (6,-2), axis of symmetry is x= 6 and -2 is the max.
Can you please post the original one by scanning or screenshot?
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I guess I don't understand how to determine if it goes up or don't and how that relates to max or min.
First off, they give you a "function below". That is \(f(x) = -x^2 +12x-38\). Just look at the coefficient of x^2 which is -1 and the highest degree of x 1) highest degree is 2 --> it is a parabola 2) coefficient of x^2 is -1 --> negative number means the parabola is downward. And, if it is downward, it has maximum , no minimum if it is upward ( the coefficient of x^2 is positive ), it has minimum, no maximum. |dw:1433033722652:dw|
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thank you!

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