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A parabola that opens downwards has a maximum at its vertex. One way to find it is to take the derivative of the parabola's equation (for y = x2, for example, this is y = 2x), set that to zero, and solve (2x = 0; x = 0). This works because the only horizontal tangent line of a parabola is at its vertex.
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What is the extreme point of the parabola?
It is either a maximum or minimum value depending on its downwards shape or its upwards shape
How can a quadratic function have both a maximum and a minimum point?
A quadratic function can only have either a maximum or a minimum point, not both. The shape of the graph, which is a parabola, determines this: if the parabola opens upwards (the coefficient of the (x^2) term is positive), it has a minimum point; if it opens downwards (the coefficient is negative), it has a maximum point. Therefore, a quadratic function cannot exhibit both extreme values simultaneously.
What is the optical property of a parabola?
"Any light beam moving vertically downwards in the concavity of the parabola (parallel to the axis of symmetry) will bounce off the parabola moving directly towards the focus." http://en.wikipedia.org/wiki/Parabola
How do you make a parabola graph downwards if you can't change the vertex?
Change it from positive to negative
What is maximum or minimum of a parabola depending on whether the parabola opens up or down?
Vertex
How do you know if a parabola has a minimum or maximum value?
When you look at the parabola if it opens downwards then the parabola has a maximum value (because it is the highest point on the graph) if it opens upward then the parabola has a minimum value (because it's the lowest possible point on the graph)
What is the extreme point of the parabola?
It is either a maximum or minimum value depending on its downwards shape or its upwards shape
What way does a parabola open if a is negative?
Downwards
What do you call the maximum or the minimum of a parabola?
A parabola's maximum or minimum is its vertex.
The maximum or minimum of a parabola depending on whether the parabola opens up or down?
A parabola opening up has a minimum, while a parabola opening down has a maximum.
How does the value of a variable affect the direction the parabola opens?
If the value of the variable is negative then the parabola opens downwards and when the value of variable is positive the parabola opens upward.
Where is the point on the parabola for the maximum area?
The point on the parabola where the maximum area occurs is at the vertex of the parabola. This is because the vertex represents the maximum or minimum point of a parabolic function.
How can a quadratic function have both a maximum and a minimum point?
A quadratic function can only have either a maximum or a minimum point, not both. The shape of the graph, which is a parabola, determines this: if the parabola opens upwards (the coefficient of the (x^2) term is positive), it has a minimum point; if it opens downwards (the coefficient is negative), it has a maximum point. Therefore, a quadratic function cannot exhibit both extreme values simultaneously.
What is the optical property of a parabola?
"Any light beam moving vertically downwards in the concavity of the parabola (parallel to the axis of symmetry) will bounce off the parabola moving directly towards the focus." http://en.wikipedia.org/wiki/Parabola
How do you make a parabola graph downwards if you can't change the vertex?
Change it from positive to negative
What is maximum or minimum of a parabola depending on whether the parabola opens up or down?
Vertex
What is the extreme point of a parabola?
The extreme point it the highest or lowest point of the parabola (depending if it is concave downwards or upwards). It is the point of the parabola tat is closest to the focus. the extreme point lies on the axis of symmetry.
