Question

Suppose that the equation V(t)=18.75t2 - 450t + 3200 represents the value of a car from 1964-2002. What year did the car have the least value?

Answer 1

1976

Explanation:

This parabolic graph has its minimum at the vertex.

Here the coefficients of the quadratic are a = 18.75, b = -450 and c = 3200.

The t value of the axis of symmetry is:

-450

t = ------------- = 12 (years)

2(18.75)

This parabola opens up. The vertex (and min. value) is at ( 12, V(12) ).

t = 12 years must be added to the model year 1964.

Thus, the car had the least value in 1964 + 12, or 1976.