h(d) equation. I need someone to check it for me =)

[K.ourt]

Ok guys, I did this problem, but my answer isnt checking right. So could someone please go through it and tell me what I screwed up on?

1. The path of a basketball can be modelled by the equation h(d)= -.13d^2 + d + 2, where h(d) is the height (in meters) of the basketball and d is the horizontal distance (in meters) from the playerer. How far does the ball travel horizontally before hitting the floor? Round your answer off to the nearest tenth of a meter.

So I have:

-.13d^2 + 1d +2 = 0
-.13d^2 + 1d = -2
-.13d^2 + 1d + (1/4) = -2 + (1/4)
(-.13d + (1/2))^2 = (-7/4)

and at this point I would square root, but it gives me a non-real answer. So, uhh, I missed something right?!

 

[tkhunny]

Yup. Completing the square requires awareness of the leading coefficient. It's easy if it is one (1). Anything else is a little trickier. Perhaps you never have seen it?

-.13(d^2 - (1/0.13)d + _________ - ________) = -2

1/0.13 = 7.69231
7.69231/2 = 3.84615
3.84315² = 14.7929

-.13(d^2 - (1/0.13)d + 14.7929 - 14.7929) = -2

-.13(d^2 - (1/0.13)d + 14.7929) - 0.13*(- 14.7929) = -2
-0.13*(d - 3.84615)² + 1.9231 = -2
-0.13*(d - 3.84615)² = - 3.9231
(d - 3.84615)² = 30.1775
d - 3.84615 = 5.49341
d = 9.3396

Check It.

-.13d^2 + 1d +2
-.13(9.3396)^2 + (9.3396) +2 =
-11.3396 + 9.3396 + 2 = 0 -- Right ON!!!

 

[soroban]

Hello, K.ourt!

1. The path of a basketball can be modeled by the equation: h(d)= -0.13d² + d + 2,

where h(d) is the height (in meters) of the basketball and d is the horizontal distance from the player.

How far does the ball travel horizontally before hitting the floor?

Round your answer off to the nearest tenth of a meter.

I know that TK prefers completing-the-square to the Quadratic Formula.
Even then, he could have made it simpler for you.

Rearrange the terms: . 0.13d² - d . = . 2


Divide the equation by 0.13:

. . . . . . . 1 . . . . . . . .2
. . d² - ------ d . = . ------
. . . . . .0.13 . . . . . .0.13


Complete the square: . 1/2 of 1/0.13 = 1/0.26
. . Square: .(1/0.26)²


Add to both sides:
. . . . . . . 1 . . . . . . . 1 . . . . . . . . 2 . . . . .1
. . d² - ------ d + ---------- . = . ------ + ----------
. . . . . .0.13 . . . .(0.26)² . . . . 0.13 . . .(0.26)²


Simplify:
. . . . . . . . 1 . . . . . . . .2.04
. . . (d - -------)² . = . ---------
. . . . . . .0.26 . . . . . . (0.26)²


Take square roots:
. . . . . . . .1 . . . . . . . √2.04
. . . d - ------- . = . ± --------
. . . . . . 0.26 . . . . . . 0.26


Sole for d:
. . . . . . . . . . . . . . 1 ± √2.04
. . . . . . . . . d . = . ------------
. . . . . . . . . . . . . . . . 0.26


The positive root is: . d .= .9.33956 .≈ .9.3 m

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Of course, had we used the Quadratic Formula,
. . we would have had the answer in four seconds.

But we would have missed this wonderful opportunity
. . to see Mathematics in Action.

 

[tkhunny]

It was pretty nasty with all those decimals. Keeping track was the hardest part.