5.1.2 Properties of Quadratic Functions in Standard Form (continued) Example 3 Finding Minimum or Maximum Values
Substituting any real value of x into a quadratic equation results in a real number. Therefore, the domain of any quadratic function is all real numbers. The range of a quadratic function depends on its vertex ( h , k ) and the direction that the parabola opens. • When a parabola opens upward, the y -value of the vertex is the minimum value and the range of the function is { y | y ≥ k }, that is, all real numbers greater than or equal to the minimum. • When a parabola opens downward, the y -value of the vertex is the maximum value and the range of the function is { y | y ≤ k }, that is, all real numbers less than or equal to the maximum.
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