SOLUTION: As it leaves its support harness, a minisub takes a deep dive toward ans underwater exploration site. The dive is modeled by the function d(x)=x^2 -12x, where d(x) represents, the

Algebra ->  Absolute-value -> SOLUTION: As it leaves its support harness, a minisub takes a deep dive toward ans underwater exploration site. The dive is modeled by the function d(x)=x^2 -12x, where d(x) represents, the      Log On


   

Question 158726: As it leaves its support harness, a minisub takes a deep dive toward ans underwater exploration site. The dive is modeled by the function d(x)=x^2 -12x, where d(x) represents, the depth of the minisub in hundreds of feet at a distance of z mi from the surface ship.
How far from the mother ship did the minisub reach its deepest point? Explain
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
There are several ways to approach this. If you are familiar with derivatives. take the first derivative and solve for 0.
If you prefer to plot and see
graph%28400%2C400%2C-10%2C10%2C-100%2C10%2C+x%5E2-12x%29
If you want to use just an algebraic approach, note that the equation is in the form of a parabola. Then either use the formauls for the vertex or find the zeros and then follow the verticla line that is halfway between those two points. For this equatuon, the zeros can be found by solving for 0+=+x%5E2-12x
0+=+x%28x-12%29
So there are zeros at x = 0 and x=12. The point halfway between them is x=6. So the vertex is on the vertical line x=6. Solving yields p%286%29+=+6%5E2+-+6%2A12
p%286%29+=+36+-+72
p%286%29+=+-36
All of the methods will get you to the answer x=6