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4 votes
Suppose that the equation

V = 20x² - 363.2x+2500 represents the value of a car from2010 - 2025.
What year did the car have the least value?
(x = 0 in 2010)

User Yastanub
by
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1 Answer

7 votes

Answer: 2019.08

Step-by-step explanation: To find the year when the car had the least value, we need to find the minimum value of the quadratic function V = 20x² - 363.2x + 2500, where x represents the number of years since 2010.

One way to find the minimum value is to use the formula for the vertex of a quadratic function, which is given by:

x = -b / (2a)

where a is the coefficient of the x² term, b is the coefficient of the x term, and x is the x-coordinate of the vertex.

In this case, a = 20 and b = -363.2, so we have:

x = -(-363.2) / (2 x 20)

x = 9.08

This means that the vertex of the parabola occurs at x = 9.08, which represents the year 2010 + 9.08 = 2019.08 (rounded to two decimal places).

Therefore, the car had the least value in the year 2019.

User Vintuwei
by
8.6k points