Final answer:
The vertex of the quadratic function representing the home's value is approximately (7.0769, 1441753.47), indicating the home's value will peak at roughly $1,441,753.47 around mid-2027.
Step-by-step explanation:
The question relates to finding the vertex of the quadratic function V(x) = 325x^2 - 4600x + 1450004, which represents the value of a home in a volatile housing market, with x being each year after 2020. To find the vertex of a quadratic function in the form ax^2 + bx + c, we use the formula x = -b/(2a) for the x-coordinate of the vertex, and then plug this value into the function to find the y-coordinate.
Applying this formula to our function:
- x-coordinate of vertex: x = -(-4600) / (2 * 325) = 4600 / 650 = 7.0769 (which means the year 2027.0769 or roughly in the middle of 2027).
- y-coordinate of vertex: V(7.0769) = 325(7.0769)^2 - 4600(7.0769) + 1450004 ≈ $1441753.47.
The vertex is approximately (7.0769, 1441753.47), which indicates that the maximum value of the home will occur around mid-2027 with an estimated value of approximately $1,441,753.47, assuming the model holds true.