SOLUTION: The value of a share of I.J. Solar can be represtented by V(x)=x^2-6x+13, where x is the number of months after January 2004. What is the lowest value V(x) will reach and when did

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The value of a share of I.J. Solar can be represtented by V(x)=x^2-6x+13, where x is the number of months after January 2004. What is the lowest value V(x) will reach and when did       Log On


   

Question 191813: The value of a share of I.J. Solar can be represtented by V(x)=x^2-6x+13, where x is the number of months after January 2004. What is the lowest value V(x) will reach and when did that occur?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
V%28x%29+=+x%5E2-6x%2B13 Find the minimum value of x.
The minimum value of x will occur at the vertex of the upward-opening parabola.
This is found by:
x+=+%28-b%29%2F2a where a = 1 and b = -6, so...
x+=+-%28-6%29%2F2%281%29
highlight%28x+=+3%29
The lowest value of V(x) is found by substituting the minimum value of x (x = 3) into the given function V%28x%29+=+x%5E2-6x%2B13 and solving for V.
V%28x%29+=+x%5E2-6x%2B13 Substitute x = 3.
V%283%29+=+%283%29%5E2-6%283%29%2B13 Simplify.
V%283%29+=+9-18%2B13
V%283%29+=+22-18
V%283%29+=+4
The lowest value of V(x) is 4.
Since x = the number of months after January, 2004, the lowest value of V(x) will be January + 3 months or April of 2004.