Tuesday

September 1, 2015
Posted by **Nina** on Saturday, November 17, 2012 at 8:39pm.

- Typo and what is the question -
**Damon**, Saturday, November 17, 2012 at 8:42pmSuspect you mean

P(t) = 6 t^2 + 110 t + 3000

- Please Help! Quadratic Eqautions -
**Nina**, Saturday, November 17, 2012 at 8:44pmoh i'm sorry. i left out that part.. the question is

When will the population reach 6000?

- Please Help! Quadratic Eqautions -
**Nina**, Saturday, November 17, 2012 at 8:45pmP(t) = 6 t^2 + 110 t + 3000

- Please Help! Quadratic Eqautions -
**Damon**, Saturday, November 17, 2012 at 8:52pmwhere is it max and min or something?

If you do not know calculus, find vertex of parabola by completing the square

t^2 + 18.33 t + 500 = P/6

t^2 + 18.33 = P/6 - 500

t^2 + 18.33 + 84 = P/6 -500 +84

(t+9.17)^2 = P/6 - 416

(t+9.17)^2 = (1/6)(p-2496)

minimum at t = -9.17 and p = 2496

that is the year 2000 - 9.17 = 1991

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**Damon**, Saturday, November 17, 2012 at 8:53pmoh, hang on

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**Nina**, Saturday, November 17, 2012 at 8:54pmThe question doesn't state wheater it's a max or min

it'as grade 11 math

no I have not done calculus

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**Nina**, Saturday, November 17, 2012 at 8:55pmoh ok

- Please Help! Quadratic Eqautions -
**Damon**, Saturday, November 17, 2012 at 9:00pm6000 = 6 t^2 + 110 t + 3000

6 t^2 + 110 t = 3000

t^2 + 18.3 t - 500 = 0

t = [ -18.3 +/-sqrt(336+2000)]/2

t = [-18.3 + sqrt(2336)]2

t = [-18.3 + 48.3 ]/2

t = 15

so 2015

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**Nina**, Saturday, November 17, 2012 at 9:02pmThank you

Much Appreciated !! (Y):)

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**Nina**, Saturday, November 17, 2012 at 9:05pmHonestly, although i appreciate this help

Is there any other way to do this problem. I think this is a little to advanced because i really don't understand it.

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**Nina**, Saturday, November 17, 2012 at 9:05pmtoo*

- Please Help! Quadratic Eqautions -
**mathgeekdude**, Saturday, November 17, 2012 at 9:39pmYou can go Damon's way, or the graphing way/ comnpleting the square binomial way or you can go quadratic

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**Steve**, Saturday, November 17, 2012 at 10:07pm6 t^2 + 110 t + 3000

if you're starting to study quadratics, you have surely used the quadratic formula to find the roots.

As Damon showed,

t = [-18.3 + 48.3 ]/2

or

t = -9.15 ± √24.14

You know the parabola is symmetric, and the vertex is midway between the roots. Note that the roots are equally spaced around t = -9.15

so, the vertex is at t = -9.15. That will be the min or max.

If none of this makes any sense, you just need to study the quadratic formula some more. There are lots of examples online, and surely some in your class materials. If all that still makes no sense, no written explanation will be any clearer; some in-person help will help clear things up.

Also, a visit to

http://rechneronline.de/function-graphs

will let you play around with various formulas and see what happens when you change stuff.