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The value of x for maximum/minimum value of a quadratic equation represents the x-coordinate of the vertex of the parabola. This point indicates either the highest or lowest value of the quadratic function, depending on whether the coefficient 'a' is negative or positive.
The calculator uses the formula:
Where:
Explanation: This formula is derived from completing the square method and gives the x-coordinate of the vertex of the parabola represented by the quadratic equation.
Details: Finding the maximum or minimum value of a quadratic function is crucial in optimization problems, physics applications, economics, engineering, and various real-world scenarios where we need to find optimal solutions.
Tips: Enter the numerical coefficients a and b of the quadratic equation in the form ax² + bx + c. The coefficient a must be non-zero for the calculation to be valid.
Q1: What does the result represent?
A: The result represents the x-coordinate of the vertex of the parabola, which is either the maximum or minimum point depending on the sign of coefficient a.
Q2: How do I know if it's a maximum or minimum?
A: If coefficient a is positive, the vertex represents a minimum point. If coefficient a is negative, the vertex represents a maximum point.
Q3: What if coefficient a is zero?
A: If a = 0, the equation is not quadratic but linear, and this formula does not apply as linear functions don't have maximum/minimum points (unless constant).
Q4: Can this be used for any quadratic equation?
A: Yes, this formula works for any quadratic equation in the standard form ax² + bx + c = 0, regardless of the values of the coefficients.
Q5: How do I find the actual maximum/minimum value?
A: Substitute the x-value back into the original quadratic equation to find the corresponding y-value, which is the actual maximum or minimum value.