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Finding the Minimum Value of
To find the minimum value of the quadratic equation , determine the coordinates of its vertex.
Since the coefficient is positive, the parabola opens upward, meaning the equation has a minimum value. Find the axis of symmetry: Use the formula . With and , . The axis of symmetry is the line . Find the vertex: Substitute into the equation to find : . The vertex is .
Because the parabola has a minimum, the -coordinate of the vertex is the minimum -value of the quadratic equation. The minimum value is , and it occurs when .
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Ch.10 Quadratic Equations - Elementary Algebra @ OpenStax
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