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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 extreme point on a parabola?
The highest or lowest point of the parabola, it is the point that is closest to the focus. The extreme point lies on the axis of symmetry
How can you tell the difference graph or function?
A function describes the relationship between two or more variables. A graph is a kind of visual representation of one or more function. A line or curve seen on a graph is called the graph of a function. * * * * * For any point in the domain, a function can map to only ine point in the range or codomain. In simpler terms, it means that (for a two dimensional graph), a vertical line can intersect the graph of the function in at most one point.
What is the extreme point on a pendulum swing?
Apogee
What are the extreme values of 2x2-8x plus 9?
Given: f(x) = 2x2 - 8x + 9 This function describes a parabola, which only has one extreme value. To find that value, you can take the derivative of the function, and use that to find the point at which it has a slope of zero: f'(x) = 4x - 8 if f'(x) = 0, then: 0 = 4x - 8 ∴4x = 8 ∴ x = 2 Now we work out the corresponding value for f(2): f(2) = 2(2)2 - 8(2) + 9 = 8 - 16 + 9 = 1 So the extreme value for this function is 1, which occurs at the point (2, 1)
