the function y=-0.296x^2+2.7x models the length x and height y that your sisters rabbit can jump in centimeters. how high does the rabbit jump? what is the length of the jump?

Question

austinl · Answer

Ok, do you have a graphing calculator?

tester97 · Answer

yup ^_^ who doesnt?

bibby · Answer

do you have an internet connection? http://www.wolframalpha.com/input/?i=y%3D-1.26%2B2.7x

austinl · Answer

Wrong equation bud.

tester97 · Answer

bibbeh did u realy just ask me that?

bibby · Answer

I copied it letter for letter. you have to mess with the parentheses

austinl · Answer

I am trying to figure out how to do this algebraically again.
I know how to do it with calculus easily!
And there is an x^2 bibsy.

bibby · Answer

woah what. I literally copied y=-0.296x^2+2.7x into wolfram. Technology has betrayed me.
Go forth austin

austinl · Answer

Okay, okay I think I got this.

We can use the formula,

$\displaystyle x=\frac{-b}{2a}$

When we have,

$y=-ax^2+bx$

Then we can plug it back into the original equation and solve for y. That will be your maximum value.
Make sense?

tester97 · Answer

so i have to move the b and a over?

austinl · Answer

No, they are literally given to you in your initial problem. Look at the general form that I posted and look at your equation. Don't they look similar? a&b are merely coefficients.

tester97 · Answer

sorry this is not making any sense to me whatsoever..its just one of those days

austinl · Answer

$y=\color{red}{-0.296}x^2+\color{blue}{2.7}x$

$y=\color{red}{-a}x^2+\color{blue}{b}x$

tester97 · Answer

oh yea i understood that part

austinl · Answer

Okay, now plug that into the little formula that I gave you.

tester97 · Answer

$$x= \frac{ -2.7 }{ -0.296 }$$

austinl · Answer

x=-b/(2a)

tester97 · Answer

whoops i forgot to multiply the denominator by 2

tester97 · Answer

so it would be $$x=\frac{ -2.7 }{2(-0.296)  }$$

austinl · Answer

Excuse me, I believe I made an error....

Maximum value is,

$\displaystyle max=c-\frac{b^2}{4a}$

Where,

$y=-ax^2+bx+c$

In our case, c=0

Sorry about that :(

tester97 · Answer

so pretty much i would just have to square the b and instead of multiplyin a by 2 it would b 4?

austinl · Answer

Yeah, sorry again.

tester97 · Answer

its ok :D let me work this out rite quick

tester97 · Answer

-6.15?

tester97 · Answer

oh wait no its not negative so it would just b 6.15?

austinl · Answer

That is what I get, but remember it is -(-6.15), so 6.15

austinl · Answer

Beat me to it :P

austinl · Answer

Then to find the distance, you would just find the x intercepts. The zeros.

tester97 · Answer

how do i do that|?

austinl · Answer

I believe you could use the quadratic formula.
I will brb, try that and I will check back shortly.

tester97 · Answer

ok

tester97 · Answer

wait would i need to just find the vertex?

tester97 · Answer

or did we already do that?

austinl · Answer

That was how high, we want to know how far now.

tester97 · Answer

oh 9.14 cm?

austinl · Answer

For some reason I keep getting zero....

But on my calculator is giving me 9.12162

tester97 · Answer

ehh about the same thanks austin ^_^

austinl · Answer

No problem! Good job btw!

terenzreignz · Answer

Oh, the repugnant smell of uncertainty... I detect a hint of it here :>

austinl · Answer

Shhhh @terenzreignz 
I corrected course......

terenzreignz · Answer

When did I ever doubt you? :D

tester97 · Answer

tj is that u?

terenzreignz · Answer

Let me check...

terenzreignz · Answer

<looks around> 
Yup, I'm pretty sure my name is TJ, one way or another, since those two letters adorn quite  a few select nooks in my room :>

tester97 · Answer

oh tj :P