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AonZ
Group Title
Help please :)
Find the values of a and b if the parabola y=a(x+b)^2 −8 has tangent y = 2x at the point P(4, 8),
 one year ago
 one year ago
AonZ Group Title
Help please :) Find the values of a and b if the parabola y=a(x+b)^2 −8 has tangent y = 2x at the point P(4, 8),
 one year ago
 one year ago

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AonZ Group TitleBest ResponseYou've already chosen the best response.0
i have gotten gradient to be 2a(x+b)
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
ok great so far y' at (x,y)=(4,8) is 2a(4+b)=8a+2b And we are also given at that point we have y'=2x But that point is (4,8) so at that point we have y'=8 So this means we have 8=8a+2b Did you get this far?
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
We should be looking for another liner equation
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Any ideas?
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
i got 8=8a +2ab
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Well you also know (4,8) is on the parabola. See if you can use that.
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
this should give you two equations with the only unknowns a and b
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
You know how to solve a system of equations, correct?
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Did you think to do 8=a(4+b)^28
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
i got 8=8a +2ab not 8=8a +2b btw
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
wait how did you get the first equation?
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
oh wait i messed up when i wrote it
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
2a(4+b)=8a+2b I didn't distribute there correctly 8a+2ab would be correct
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
so yeah we have 8a+2ab=8
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
2nd equation is 16a + 8ba + ab^2  16 right?
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
all of that = 0 yes
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
then we just solve right?
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
16a + 8ba + ab^2  16 = 0 and 8a+2ab8= 0 err how?
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Did you try solving the linear equation either for a or b and replace the a or b in the first equation you ahve there
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
im pretty sure we made a mistake somewhere
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=16a+%2B+8ba+%2B+ab%5E2++16+%3D+0++and++8a2ab8%3D+0
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
the answers in the back of my book says 1/16 = a and 12= b
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
why did you change the sign in that one equation?
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
oh typed it wrong before
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
can we start from the begining again?
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
the derivative is 8a+2ab that means the gradient is 8a + 2ab How did it become 8= 8a + 2ab
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
y'=2x at (4,8)
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
we also know that y'=2a(x+b) at (4,8) so at (4,8) we know 2x=2a(x+b)
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
x=4 then
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
so we have 2*4=2a(4+b)
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
8=8a+2ab
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
your book's answer doesn't make sense
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
so if a=1/16, b=12 and we have that y'=2x at (4,8) and y'=2a(x+b) at (4,8) then we have 2*4=2*1/16(4+12) correct? is this true?
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
2*4=8 2/16*(4+12)=1/8*(16)=2 2 does not equal 8
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
The equation you put is correct right? y=a(x+b)^28
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
the point is (4,8) where we have the tangent line y=2x
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
yes right question
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
i see nothing wrong with our resulting equations
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
but i dont think we could sub (4,8) into 16a + 8ba + ab^2  16=0
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
we already did to get that equation
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
remember y=a(x+b)^28 (4,8) is on that parabola
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
8=a(4+b)^28
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
a(4+b)^216=0 a(16+8b+b^2)16=0 ab^2+8ab+16a16=0
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
So we have ab^2+8ab+16a16=0 4=4a+ab
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Solve that bottom equation for either a or b then plug into the first equation.
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
By the way I just divided our earlier linear equation by 2 to get 4=4a+ab 4=a(4+b) 4/(4+b)=a Assuming b does not equal 4. Then we have 0=4/(4+b)*b^2+8*(4/(4+b))*b+16*(4/(4+b))16
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Multiply both sides by 4+b 0=4b^2+32b+6416(4+b)
 one year ago

AonZ Group TitleBest ResponseYou've already chosen the best response.0
http://au.answers.yahoo.com/question/index?qid=20130720230137AA4cCvd
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
yep so i did make a mistake there the slope of 2x is 2 I put 8. haha So we had 2=8a+2ab was suppose to be that one linear equation not 8=8a+2ab
 one year ago
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