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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 are the similarities between parabola and catenary?
The Catenary and Parabola are different curves that look similar; they are both "U" shaped and symmetrical, increasing infinitely on both sides to a minimum.
What is the maximum or minimum value of y equals x to the power of 2 minus 4x plus 7?
It has an absolute minimum at the point (2,3). It has no maximum but the ends of the graph both approach infinity.
Maximum and minimum values of quadratic formula?
maximum and minimum are both (-b/2a , c - (b^2/4a))
How is a bridge a parabola?
They both have an arc 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 the the vertex of a parabola?
The vertex would be the point where both sides of the parabola meet.
What are the similarities between parabola and catenary?
The Catenary and Parabola are different curves that look similar; they are both "U" shaped and symmetrical, increasing infinitely on both sides to a minimum.
What is the maximum or minimum value of y equals x to the power of 2 minus 4x plus 7?
It has an absolute minimum at the point (2,3). It has no maximum but the ends of the graph both approach infinity.
How can a quadratic function have both a maximum and minimum point?
It can't - unless you analyze the function restricted to a certain interval.
What do crests and troughs have in common?
Crests and troughs are both characteristic features of waves. A crest is the point on a wave with the maximum positive amplitude, while a trough is the point with the maximum negative amplitude. Together, they represent the maximum and minimum points of a wave's oscillation.
Maximum and minimum values of quadratic formula?
maximum and minimum are both (-b/2a , c - (b^2/4a))
What is the directrix of a parabola?
"From the geometric point of view, the given point is the focus of the parabola and the given line is its directrix. It can be shown that the line of symmetry of the parabola is the line perpendicular to the directrix through the focus. The vertex of the parabola is the point of the parabola that is closest to both the focus and directrix."-http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/parabola.htm"A line perpendicular to the axis of symmetry used in the definition of a parabola. A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus, or set of points, such that the distance to the focus equals the distance to the directrix."-http://www.mathwords.com/d/directrix_parabola.htm
How do you find the minimum or maximum of a function and example?
It depends on the function. Some functions, for example any polynomial of odd order, will have no maximum or minimum. Some functions, such as the sine or cosine functions, will have an infinite number of maxima and minima. If a function is differentiable then a turning point can be found by finding the zero of its derivative. This could be a maximum, minimum or a point of inflexion. If the derivative before this zero is negative and after the zero is positive then the point is a minimum. If it goes from positive to negative, the pont is a maximum, and if it has the same sign (either both +ve or both -ve) then it is a point of inflexion. A second derivative can help answer this quicker, but it need not exist. These are all well behaved functions. The task is much more complicated for ill behaved functions. Consider, for example, the difference between consecutive primes. The minimum is clearly 1 (between 2 and 3) but the maximum? Or the number of digits between 1 and 4 in the decimal expansio of pi = 3.14159.... Minimum digit between = 0 (they are consecutive near the start of pi), but maximum?
How is a bridge a parabola?
They both have an arc shape.
What is the maximum value that the graph of ycosx assume?
Both the function "cos x" and the function "sin x" have a maximum value of 1, and a minimum value of -1.
Why alcohol is used in maximum minimum thermometer?
alchohol has lower freezing point so it is used in minimum bulb,as it contracts the mercury bar rises in the minimum bulb..
