SOLUTION: Hi guys! So we have these quadratic equation word problems that we are solving right now. The problem I am about to list is one that I think I finished and got right, but I'm not e

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi guys! So we have these quadratic equation word problems that we are solving right now. The problem I am about to list is one that I think I finished and got right, but I'm not e      Log On


   

Question 1017786: Hi guys! So we have these quadratic equation word problems that we are solving right now. The problem I am about to list is one that I think I finished and got right, but I'm not entirely sure. Here is the problem and the answer that I got so you can check and help me:
You are trying to dunk a basketball. You need to jump 2.5 ft in the air to dunk the ball. The height that your feet are above the ground is given by the function h(t) = -16(t)^2 + 12t. What is the maximum height that your feet will be above the ground? Will you be able to dunk the basketball?
I completed the square where I found a a new "c" (9/64) and once I squared it, I got 3 plus or minus 3 all over 8. So basically, 3+-3/8. I got 0 when I subtracted, making that an extraneous solution. When I added 3 with 3, I got 6/8 which becomes 3/4. Does that mean 3/4 of a foot like I think it does? Thank you!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
16t%5E2-12t is part of the perfect square
16t%5E2-12t%2B9%2F4=%284t%29%5E2-2%284t%29%283%2F2%29%2B%283%2F2%29%5E2=%284t-3%2F2%29%5E2 ,
so -16t%5E2%2B12t-9%2F4=-%284t-3%2F2%29%5E2 , and
.

In words, the maximum of h%28t%29 is 2.25ft .
Your feet will not be any higher than 2.25ft above the ground,
so you will not be able to dunk the basketball.