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Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationMaximum & minimum valuesMedium2 minai-gemini

MathematicsMediumsingle choice

The minimum value of the quadratic expression $x^{2} - 4 x + 7$ is:

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Answer:

Solution:

The given quadratic expression is $f (x) = x^{2} - 4 x + 7$ . This is a parabola opening upwards, so its minimum value occurs at the vertex. The x-coordinate of the vertex is $x = - \frac{b}{2 a} = - \frac{- 4}{2 ( 1 )} = 2$ . Substituting $x = 2$ into the expression, we get $f (2) = (2)^{2} - 4 (2) + 7 = 4 - 8 + 7 = 3$ .

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Maximum & minimum values

⏱ 2mℹ️ Source: ai-gemini

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