Question

The value in dollars of a new car is modeled by the function V (t)=125t^2- 3,000 t + 22,000, where t represents the number of years since it was purchased. Determine the age of the car when its value is at a minimum and maximum.

Answer 1

obviously this is a parabola since x is squared. since the coefficient of x^2 is positive that means that the ends of the parabola go up. this means that the vertex is the lowest point in the graph. to find the x value ofnthe vertex we use the the quadratic equation but take out the square root part. so:
x = -b/2a
b = -3000
a = 125

x = -(-3000) / (2 * 125)
x = 3000 / 250
x = 12

plug 12 into equation for x. I put x instead of t. But but it is the same

V = 125 (12)^2 -3000 (12) + 22000
V = 4000.

So so low value is 4000 after 12 years.

I am not sure about a max value because the end of the parabola goes up forever. if there is a stipulation that once the car hits 12 years and is at its minimum then the car value never changes, then the max value would be at the 0 year at the time of purchase. And that would make it 22000. But I will not say max for sure because I do not see a stipulation