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What name is given to the turning point also known as the maximum or minimum of the graph of a quadratic function?
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∙ 8y ago
vertex
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What things are significant about the vertex of a quadratic function?
It is a turning point. It lies on the axis of symmetry.
Parts of a parabola?
There's the vertex (turning point), axis of symmetry, the roots, the maximum or minimum, and of course the parabola which is the curve.
Do all polynomials have at least one minimum?
Polynomials of an even degree will always have either a minimum point, or a maximum point, or both.Polynomials of an odd degree may or may not have minima or maxima. If, for example, a polynomial function is simply a transformation of xn, there will be no turning points. For example:f(x) = x5 + 5x4 + 10x3 + 10x2 + 5x + 1 = (x+1)5f'(x) = 5(x+1)4There is only one solution for f'(x) = 0, which is of course x = -1. Since the range of f(x) includes all the real numbers, it follows that this solution represents a point of inflection, and not a turning point.If a polynomial of odd degree does have any turning points, it will have at least one minimum point. It cannot have maximum points only.* * * * *Polynomials of an odd degree cannot have a global maximum or minimum because if the leading coefficient is positive, it goes asymptotically from minus infinity to plus infinity and the other way around if the leading coefficient is negative.
When the graph of a quadratic equation has its turning point on the x-axis how many roots does it have?
It will have two equal roots.
What function of spanner?
spanner provides grip in applying torque to turn objects such as nuts and bolts-or keep them from turning.
How to compute the minimum and maximum function values of a quadratic function?
Suppose you have a quadratic function of the form y = ax2 + bx + c where a, b and c are real numbers and a is non-zero. [If a = 0 it is not a quadratic!] The turning point for this function may be obtained by differentiating the equation with respect to x, or by completing the squares. However you get there, the turning point is the solution to 2ax + b = 0 or x = -b/2a Now, if a > 0 then the quadratic has a minimum at x = -b/2a and it has no maximum because y tends to +∞ as x tends to ±∞ . if a < 0 then the quadratic has a maximum at x = -b/2a and it has no minimum because y tends to -∞ as x tends to ±∞. You evaluate the value of y at this point. y = a(-b/2a)2 + b(-b/2a) + c = b2/4a - b2/2a + c = -b2/4a + c = -(b2 - 4ac)/4a In either case, if the domain of the function is bounded on both sides, then the missing extremum will be at one or the other bound - whichever is further away from (-b/2a).
What is the turning point in the graph of a quadratic function?
The answer depends on the form in which the quadratic function is given. If it is y = ax2 + bx + c then the x-coordinate of the turning point is -b/(2a)
What things are significant about the vertex of a quadratic function?
It is a turning point. It lies on the axis of symmetry.
What is The turning point of a parabola?
the vertex, or very bottom point.I can also be called the maximum or minimum.
How do you find the salient feature in a graph?
Depending on the graph, for a quadratic function the salient features are: X- intercept, Y-intercept and the turning point.
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?
Parts of a parabola?
There's the vertex (turning point), axis of symmetry, the roots, the maximum or minimum, and of course the parabola which is the curve.
What is the maxima or minima for the line y equals mx plus c?
A straight line has no turning points and so no local maxima or minima. The line has a maximum at + infinity and a minimum at - infinity if m > 0 and conversely if m < 0. When m = 0, the line is horizontal and so has no maximum or minimum. ([Alternatively, every point on the line is simultaneously a maximum and a minimum.]
Which constant tells you what the value of maximum and minimum?
Not a constant, but the differential, i.e. gradient, of the equation. It = 0 at maxima and minima, where the curve is at its turning-point(s).
Do all polynomials have at least one minimum?
Polynomials of an even degree will always have either a minimum point, or a maximum point, or both.Polynomials of an odd degree may or may not have minima or maxima. If, for example, a polynomial function is simply a transformation of xn, there will be no turning points. For example:f(x) = x5 + 5x4 + 10x3 + 10x2 + 5x + 1 = (x+1)5f'(x) = 5(x+1)4There is only one solution for f'(x) = 0, which is of course x = -1. Since the range of f(x) includes all the real numbers, it follows that this solution represents a point of inflection, and not a turning point.If a polynomial of odd degree does have any turning points, it will have at least one minimum point. It cannot have maximum points only.* * * * *Polynomials of an odd degree cannot have a global maximum or minimum because if the leading coefficient is positive, it goes asymptotically from minus infinity to plus infinity and the other way around if the leading coefficient is negative.
When is Maximum Ride turning into a movie?
2013
When the graph of a quadratic equation has its turning point on the x-axis how many roots does it have?
It will have two equal roots.
