Final answer:
The domain of the quadratic function is all real numbers. The range depends on whether the parabola opens upwards or downwards: it could be either [2, ∞) or (-∞, 2]. Without additional information, the precise range cannot be determined.
Step-by-step explanation:
Finding the Range and Domain of a Quadratic Function
The question asks to find the domain and range of a quadratic function with a given vertex at (0,2). Let's denote this function as f(x).
Domain: The domain of any quadratic function is all real numbers because a parabola extends infinitely in both directions on the x-axis. For a quadratic function f(x) = ax² + bx + c, there are no restrictions on x, so the domain is (-∞, ∞).
Range: To find the range, we need to know if the parabola opens upwards or downwards. Since only the vertex is provided, we'll consider both cases:
- If the parabola opens upwards, the range is [2, ∞) because the lowest point on the graph is the vertex at (0,2).
- If the parabola opens downwards, the range is (-∞, 2] because the highest point on the graph is the vertex at (0,2).
Without the equation of the quadratic function or additional information on whether the coefficient of the x² term is positive or negative, we cannot conclusively determine the range. However, the domain remains all real numbers.