Question

Given the domain and range of the quadratic function whose graph is described with a vertex at (-1, -7) and the parabola opens upward, please provide the domain and range for this function. You can refer to the attached graph for reference.

Answer 1

The domain of the quadratic function with a vertex at (-1, -7) and an upward opening parabola is all real numbers. The range is from -7 to positive infinity.

Step-by-step explanation:

The domain of a quadratic function is all real numbers since, for any x-value, we can find a corresponding y-value. Specifically, for the quadratic function with a vertex at (-1, -7) that opens upwards, the domain is all real numbers, which we can denote as (-∞, +∞).

Considering the vertex is the lowest point on the graph because the parabola opens upward, the range of the function starts from the y-coordinate of the vertex and goes to positive infinity. Thus, the range can be expressed as [-7, +∞).

Remember, the vertex represents the minimum point of the parabola since it opens upward. Always consider the direction of the parabola's opening when determining the range of a quadratic function. The domain remains the same for any parabola because it can extend indefinitely along the x-axis.