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Find the value of x at which y is Maxima or minima y = (x - 1)^2?
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Find the value of x at which y is Maxima or minima y = (x - 1)^2?
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Find the value of x at which y is Maxima or minima y = (x - 1)^2?
Finding the Maximum or Minimum of a Quadratic Function
To find the value of x at which y is a maximum or minimum in the function y = (x - 1)^2, we need to determine the vertex of the parabola formed by the quadratic function.
Finding the Vertex
- The vertex of a parabola in the form y = a(x - h)^2 + k is located at the point (h, k).
- In the given function y = (x - 1)^2, the vertex is at (1, 0).
Determining the Nature of the Vertex
- Since the coefficient of the x^2 term is positive in the given function, the parabola opens upwards.
- This means that the vertex at (1, 0) represents the minimum value of the function.
Conclusion
- The value of x at which y is a minimum in the function y = (x - 1)^2 is x = 1.
- At x = 1, y will be at its minimum value of 0.
- Therefore, 1 is the value of x at which y is a minimum in the given quadratic function.
To find the value of x at which y is a maximum or minimum in the function y = (x - 1)^2, we need to determine the vertex of the parabola formed by the quadratic function.
Finding the Vertex
- The vertex of a parabola in the form y = a(x - h)^2 + k is located at the point (h, k).
- In the given function y = (x - 1)^2, the vertex is at (1, 0).
Determining the Nature of the Vertex
- Since the coefficient of the x^2 term is positive in the given function, the parabola opens upwards.
- This means that the vertex at (1, 0) represents the minimum value of the function.
Conclusion
- The value of x at which y is a minimum in the function y = (x - 1)^2 is x = 1.
- At x = 1, y will be at its minimum value of 0.
- Therefore, 1 is the value of x at which y is a minimum in the given quadratic function.
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Find the value of x at which y is Maxima or minima y = (x - 1)^2?
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Find the value of x at which y is Maxima or minima y = (x - 1)^2? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Find the value of x at which y is Maxima or minima y = (x - 1)^2? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of x at which y is Maxima or minima y = (x - 1)^2?.
Find the value of x at which y is Maxima or minima y = (x - 1)^2? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Find the value of x at which y is Maxima or minima y = (x - 1)^2? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of x at which y is Maxima or minima y = (x - 1)^2?.
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