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Maximum Minimum Value of Quadratic Expression: Quadratic Equations Video Lecture | CSAT Preparation - UPSC

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FAQs on Maximum Minimum Value of Quadratic Expression: Quadratic Equations Video Lecture - CSAT Preparation - UPSC

1. What is the maximum value of a quadratic expression?
Ans. The maximum value of a quadratic expression occurs when the coefficient of the quadratic term (i.e., the term with the variable raised to the power of 2) is negative. In this case, the maximum value is equal to the y-coordinate of the vertex of the parabola represented by the quadratic expression.
2. How can I find the minimum value of a quadratic expression?
Ans. To find the minimum value of a quadratic expression, determine the vertex of the parabola represented by the expression. The x-coordinate of the vertex can be found by using the formula -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively. Then substitute the x-coordinate into the quadratic expression to find the corresponding y-coordinate, which represents the minimum value.
3. Can a quadratic expression have both a maximum and a minimum value?
Ans. No, a quadratic expression can have either a maximum or a minimum value, but not both. Whether the quadratic expression has a maximum or a minimum depends on the coefficient of the quadratic term. If it is positive, the expression has a minimum value, and if it is negative, the expression has a maximum value.
4. Is there a direct formula to find the maximum or minimum value of a quadratic expression?
Ans. Yes, there is a direct formula to find the maximum or minimum value of a quadratic expression. It is given by -D/4a, where D is the discriminant of the quadratic expression and a is the coefficient of the quadratic term. However, this formula can only be used when the quadratic expression is in standard form (ax^2 + bx + c = 0).
5. How can I determine whether a quadratic expression has a maximum or minimum value without graphing it?
Ans. To determine whether a quadratic expression has a maximum or minimum value without graphing it, you can look at the coefficient of the quadratic term. If it is positive, the expression opens upward and has a minimum value. If it is negative, the expression opens downward and has a maximum value.
207 videos|156 docs|192 tests
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