In a volatile housing market, the overall value of a home can be modeled by v(x) = 325x2 – 4600x + 145000, where v represents th

Question

3 years ago

5

In a volatile housing market, the overall value of a home can be modeled by v(x) = 325x2 – 4600x + 145000, where v represents th

e value of the home and x represents each year after 2020. find the vertex and interpret what the vertex of this function means in terms of the value of the home. show the work you completed to determine the vertex

Mathematics

1 answer:

alekssr [168] · Answer 1 · 2022-12-15T09:11:40+03:00

The vertex of the housing market function is its maximum value

The vertex of the function is (7.1, 128723.25) and it means that the overall value of a home is at the highest in 2027 at a price of #128723.25

<h3>How to determine the vertex?</h3>

The function is given as:

v(x) = 325x^2 - 4600x + 145000

Differentiate

v'(x) = 2*325x - 4600

Set to 0

2*325x - 4600 = 0

Collect like terms

2*325x = 4600

Solve for x

x = 7.1

Substitute 7.1 in V(x)

v(7.1) = 325*7.1^2 - 4600*7.1 + 145000

v(7.1) = 128723.25

Hence, the vertex of the function is (7.1, 128723.25) and it means that the overall value of a home is at the highest in 2027 at a price of #128723.25