" Quadratic Word Problems! "
SADst testing test asd testing teststst.Hey guys, it's me, Elven. Sorry if the post took a while to get on, it took me a while to figure out how to log in, then when I did, I forgot my password -.- , blah blah, then I had to figure how to use this post thingy. Don't get fustrated! This is my first time posting! Sooo ...........
For Quadratic word problems, " THERE ARE 3 MAJOR TYPES OF PROBLEMS "
#1 - One thing will INCREASE while another thing will DECREASE
Example,
Computer software sells for $20 each, 300 people will purchase at that price. For every 5 dollar increase, 30 fewer people will purchase. What is the maximum revenue? [ Trying to find vertex ]
[ Revenue - Price X number sold ]
Price --> 20 + 5x [ 20 is from the $20, +5 is the 5 dollar increase, and 'x' is the variable. It is going up. ]
Sold --> 300 - 30x [ 300 are the people, -30 is the fewer people purchasing, 'x' is the variable. It is going down. ]
and so... R = (20+5x)(300-30x)
= 6000 - 600x + 1500x - 150x²
= 600 + 900x - 150x² [ And now you have to rewrite this in the x2 + x + # so it is factorable ]
= -150x² + 900x + 600 [ Now you want to complete the square, *Negative coefficient = going downwards. ]
= -150(x² - 6x + _____ ) + 6000 [ Factored out 150, now to find 3rd term, divide mid. term by 2, then square ]
( 6/2 = 3² = 9 )
= -150(x² - 6x + __9__ ) + 6000 [ What you really put in the brackets was -150(9) = -1350 so to keep it balanced on the outside of brackets, you add 1350 ]
= -150(x² - 6x + __9__ ) + 6000 + 1350 [ Now you have to convert it to a(x-h)² + k ]
= -150(x-3)² + 7350 [ Now that you know the variable, you'd want to plug in the information ]
20 + 5(3) = 35
300 - 30(3) = 210
.. (35)(210) = 7350
*If you go back and check the y vertex, it is the same as the answer. o0o lala.
#2 - Ussually (always) you are finding a maximum area based on a linear amount of fencing, string, rope. [ Basically anything that is enclosing ]
Example,
What is the maximum rectangular area that can be enclosed by 120m of fencing, if one side of the rectangle is an existing wall?
-- ** ~~ !!!HINT OMG!!! ~~ ** -- .... DRAW A DIAGRAM ....
Here is my beautiful diagram
ok as you can see, i named the left and right side " W " and " L " isthe bottom side, Which is ..
120m subtracted by the 2 sides, which is W .. [ Trying to find vertex ]
To find the area ... [ A = lXw ]
So (120-2w)(W)
= 120w-2w² [ Rewrite, just as I did above ]
= -2w² + 120w [ Factor and complete the square]
= -2(w² - 60w + _____ ) + 0 [ Mid. term divided by 2, then squared ]
( 60/2 = 30² = 900 )
= -2(w² - 60w + __900__ ) + 1800 [ Actually added -1800 in the brackets, so balancing out you add 1800 outside brackets. Now you convert to a(x-h)² + k ]
= -2(w-30)² + 1800
[ Vertex = (30, 1800) ]
Now to plug in the information ...
W = 30
L = 120 - 2(30) = 60
(30)(60) = 1800
*Wow! Once again equaling the y vertex. MIND BLOGGLING!!
#3 - [ GIVEN AN EQUATION ]
Ussually something shot inro the air or dropped from a height.
Example,
A projectile is shot straight up from a height of 6m with initial velocity of 80m/s. It's height is given by the equation.
h = 6 + 80 - 5t² [ If you're spending time wondering where the 5 came from, the equation was given along with the question .. Like the title says ' GIVEN AN EQUATION ' ]
After how many seconds will it reach it's maximum height? What is that height? [ Eaazzzy pweeezzy, we got the equation so .. ]
H = 6 + 80 - 5t² [ Now you ' rewrite the sucker ' words of Ingram ]
H = -5t² + 80t + 6 [ Facter and complete square ]
= -5(t² -16t + _____ ) + 6
( -16/2 = (-8)² = 64 )
= -5(t² - 16 + __64__ ) + 6 + 320 [ Balancing outside and inside brackets. Then convert to a(x-h)² + K ]
= -5(t-8)² + 326
So the time it will take to reach the maximum height is 8 seconds [ X point of vertex ]
And the maximum height is 326m [ Y point of vertex ]
I'm DONE! YES! I think thats all.. Whew. Thanks for reading .. if you did -.- ... Oh man im hungry! I'm out.
Oh yeah, almost forgot. Next poster or whatever you guys call it will be swan. I mean Xuan Bwhahahaha!!! x)
P.S. Correct any mistakes for me please and thanks.
Labels: Testing
posted by Eleven @ 6:28 PM
2 Comments:
testingignign test. woo first comment ever!
Been spending hours trying to find help for these and this is the best one, THANNNNKK YOUUU
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