$\"\"$

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The quadratic function is $\"\"$ .

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Find the maximum or minimum values.

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The standard form of quadratic function $\"\"$ , where $\"\"$ .

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Rewrite the function $\"\"$ .

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$\"\"$ and $\"\"$ .

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Since $\"\"$ , the function has a minimum value and opens upward.

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The equation of the axis symmetry is $\"\"$ .

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$\"\"$ (Substitute the values $\"\"$ and $\"\"$ )

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$\"\"$ (Simplify)

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The equation of the axis symmetry is $\"\"$ and $\"\"$ -coordinate of the vertex is $\"\"$ . $\"\"$

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Find the $\"\"$ -coordinate of the vertex by evaluating the function for $\"\"$ .

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$\"\"$ (Original function)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Evaluate powers: $\"\"$ )

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$\"\"$ (Substitute: $\"\"$ )

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The minimum value of the function is $\"\"$ .

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Find domain and range of the function.

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The domain is all real numbers.

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The range is all real numbers greater than or equal to minimum value ,or $\"\"$ .

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$\"\"$

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The function has minimum value.

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The minimum value of the function is $\"\"$ .

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The domain is all real numbers.

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The range is $\"\"$ .