SOLUTION: 3. The function h = −0.25 d² + 0.8d models the height, h meters, of a soccer ball in terms of the horizontal distance, d meters, from where the ball was kicked. a) Fi

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: 3. The function h = −0.25 d² + 0.8d models the height, h meters, of a soccer ball in terms of the horizontal distance, d meters, from where the ball was kicked. a) Fi      Log On

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Question 1177358: 3. The function h = −0.25 d² + 0.8d models the height, h meters, of a soccer ball in terms of the horizontal distance, d meters, from where the ball was kicked.

a) Find the horizontal distance the ball travels until it first hits the ground. Show work.
Use both the factoring method and the quadratic formula method to obtain your answer.

Found 2 solutions by Solver92311, MathLover1:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


The height of the ball when it hits the ground is quite obviously zero. So set your function equal to zero and solve for . Note: Since this function is quadratic, you will get two roots. Since the quadratic has no constant term, one of the roots will be zero. Consider how you should interpret a zero root in the context of this problem. If you get a different answer when you solve by factoring than when you solve using the quadratic formula, check your arithmetic because you most certainly made an arithmetic error somewhere.


John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a) Find the horizontal distance the ball travels until it first hits the ground. Show work.
Use both the factoring method and the quadratic formula method to obtain your answer.
h=+-0.25d%5E2+%2B+0.8d
when a soccer ball hits the ground,+h=0+
0=+-0.25d%5E2+%2B+0.8d......factor
0=+%28-0.25d+%2B+0.8%29d
-> d=0
-0.25d+%2B+0.8=0+
0.8=0.25d+
+d=0.8%2F0.25
d=3.2

using the quadratic formula method:

h=+-0.25d%5E2+%2B+0.8d => a=-0.25,+b=+0.8, c=0

d=%28-0.8%2B-sqrt%280.8%5E2-4%28-0.25%29%2A0%29%29%29%2F%282%28-0.25%29%29
d=%28-0.8%2B-sqrt%280.8%5E2%29%29%2F%28-0.50%29
d=%28-0.8%2B-0.8%29%2F%28-0.50%29
=>
d=%28-0.8%2B0.8%29%2F%28-0.50%29=0%2F-0.50=0
or
d=%28-0.8-0.8%29%2F%28-0.50%29=-1.6%2F-0.50=3.2->the horizontal distance the ball travels until it first hits the ground

in case you need these questions:
b) Find the horizontal distance when the ball reaches its maximum height. Make a sketch. Show work.
h=+-0.25d%5E2+%2B+0.8d
max is at vertex,
-b%2F2a=-0.8%2F%282%28-0.25%29%29=1.6
the horizontal distance when the ball reaches its maximum height is d=1.6

c) Find the maximum height of the ball using the distance you just determined in part b.
h=+-0.25%2A1.6%5E2+%2B+0.8%2A1.6+
h=+-0.25%2A1.6%5E2+%2B+0.8%2A1.6+
h=+-0.64%2B+1.28+
h=+0.64+