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AonZ
 one year ago
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),
AonZ
 one year ago
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),

This Question is Closed

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2ok 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?

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

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

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

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

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

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

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

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.22a(4+b)=8a+2b I didn't distribute there correctly 8a+2ab would be correct

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

AonZ
 one year ago
Best ResponseYou've already chosen the best response.02nd equation is 16a + 8ba + ab^2  16 right?

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

AonZ
 one year ago
Best ResponseYou've already chosen the best response.016a + 8ba + ab^2  16 = 0 and 8a+2ab8= 0 err how?

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

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

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

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

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

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

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

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

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

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2so 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?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.22*4=8 2/16*(4+12)=1/8*(16)=2 2 does not equal 8

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

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

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

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

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

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

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

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

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2By 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

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

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2yep 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
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