In a volatile housing market, the overall value of a home can be modeled by V(x) = 210x2 – 4400x + 125000, where V represents the 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.
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MrRoyal 3 months ago
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The interpretation is that the housing market reaches a maximum value of \$101952.384, 10.48 years after 2020

### How to interpret the vertex?

The function is given as:

V(x) = 210x^2 – 4400x + 125000,

Differentiate the function

V'(x) = 420x – 4400

Set to 0

420x – 4400 =0

Add 4400 to both sides

420x = 4400

Divide both sides by 420

x = 10.48

Substitute x = 10.48 in V(x) = 210x^2 – 4400x + 125000,

V(10.48) = 210(10.48)^2 – 4400(10.48) + 125000

Evaluate

V(10.48) = 101952.384

Hence, the vertex is (10.48, 101952.384)

And the interpretation is that the housing market reaches a maximum value of \$101952.384, 10.48 years after 2020