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Maxima & Minima: Quadratic Equations Video Lecture - UPSC

FAQs on Maxima & Minima: Quadratic Equations Video Lecture - UPSC

1. What is a quadratic equation?

Ans. A quadratic equation is a second-degree polynomial equation in a single variable, usually written in the form of ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

2. How do we find the maximum or minimum value of a quadratic equation?

Ans. To find the maximum or minimum value of a quadratic equation, we can use the concept of vertex and axis of symmetry. The vertex of a quadratic equation is the point where the parabola reaches its highest or lowest point. The x-coordinate of the vertex can be found using the formula x = -b/2a, and the y-coordinate can be obtained by substituting the x-coordinate into the quadratic equation.

3. What is the significance of maximum and minimum values in quadratic equations?

Ans. The maximum or minimum value of a quadratic equation represents the highest or lowest point on the graph of the equation. It provides information about the vertex or turning point of the parabola. This value is crucial in various real-life applications, such as determining the maximum profit or minimum cost in business and optimization problems.

4. Can a quadratic equation have both a maximum and a minimum value?

Ans. No, a quadratic equation can have either a maximum value or a minimum value, but not both. The nature of the parabola determines whether it opens upwards (having a minimum value) or downwards (having a maximum value). The coefficient 'a' in the quadratic equation determines the concavity of the parabola.

5. How can we determine if a quadratic equation has a maximum or minimum value?

Ans. The sign of the coefficient 'a' in a quadratic equation determines whether it has a maximum value or a minimum value. If 'a' is positive, the parabola opens upwards and has a minimum value. If 'a' is negative, the parabola opens downwards and has a maximum value. This can also be determined by examining the leading coefficient of the quadratic equation.

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Oct 22, 2025 Last updated

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