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Chapter 3: Problem 45

Give the domain and the range of each quadratic function whose graph is described. The vertex is \((-1,-2)\) and the parabola opens up.

Short Answer

Expert verified
The domain of the function is all real numbers, expressed in interval notation as \((-\infty, \infty)\). The range of the function is all real values greater than or equal to -2, expressed in interval notation as \([-2, \infty)\).

Step by step solution

01

Determine the domain of the function

The parabola is a curve that extends infinitely to the left and right. As such, the domain for any quadratic function is all real numbers. In interval notation, this is expressed as \((-\infty, \infty)\).
02

Determine the range of the function

An upward opening parabola has all real numbers greater than or equal to the y-coordinate of the vertex as its range. The y-coordinate of the vertex given is -2. Thus, the range of this function is all real numbers greater than or equal to -2. We write this in interval notation as \([-2, \infty)\).

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