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Calculus/Calculus,tangent line

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Expert: Alon Mandes - 4/19/2009


Question
Find an equation of the parabola y=ax^2+bx+c that passes through (0,1) and is tangent to the line y=x-1 at (1,0).

Answer
Let's run through the given fact & calculate a,b & c :
(1)The parabola passes through the point (0,1) . That means :
y(0)=1 -> c=1
(2) The parabola passes through another point (1,0) . That means :
y(1)=0 -> a+b+c=0 -> a+b+1=0 -> a+b=-1 .
(3) The slope of the tangent line is 1. That means :
y'(1)=1.
y'=2ax+b . Thus,
2a+b=1. & we know from equation (2) that a=-b-1, therefore :
2(-b-1)+b=1 -> -2b-2+b=1 -> b=-3 .
Let's substitute this result in eq (2) :
a-3=-1 -> a=2. Hence :
Our parabola is : y=2x^2-3x+1 .

Alon.  

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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