Final Answer:
The given information describes a quadratic function. Its vertex (v) is at the point (1.5, -6.25), and it has two additional points on the parabola: (0, -4) and (1, -6). The domain of this quadratic function is (-∞, ∞), and its range is [-6.25, ∞).
Step-by-step explanation:
The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. In this case, the vertex is provided as (1.5, -6.25), so the function can be written as f(x) = a(x - 1.5)² - 6.25.
To find the value of 'a' and complete the equation, we can use one of the given additional points. Let's use the point (0, -4):
-4 = a(0 - 1.5)² - 6.25. Solving this equation, we find that 'a' equals -2. Therefore, the quadratic function is f(x) = -2(x - 1.5)² - 6.25.
Now, let's verify the other given point (1, -6):
-6 = -2(1 - 1.5)² - 6.25. This equation is satisfied, confirming that the points lie on the quadratic function.
The domain of a quadratic function is always (-∞, ∞), and the range can be determined by analyzing the vertex. In this case, the vertex is at its lowest point, so the range is [-6.25, ∞).