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Tangent to a parabola

Given that f(x)=2x^2 +8x+3 and the line y=4x+c which is a tangent to the curve f(x).
Calculate c.
Original post by AverageJoe22
Given that f(x)=2x^2 +8x+3 and the line y=4x+c which is a tangent to the curve f(x).
Calculate c.


There will only be one point of intersection between a quadratic and its tangent. Use the discriminant?
find where y = 2x2 + 8x + 3 meets y = 4x + c

you will end up with a quadratic equation. the discriminant has to be a certain value for there to be a single solution.
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Avatar for ubisoft
ubisoft
3
Make f'(x) = 4 as you know the gradient of the tangent is 4.
Original post by the bear
find where y = 2x2 + 8x + 3 meets y = 4x + c

you will end up with a quadratic equation. the discriminant has to be a certain value for there to be a single solution.


what value?
Original post by AverageJoe22
what value?


so if D is positive you get 2 results

if D is negative you get 0 results...

i am not allowed to give complete answers
Original post by the bear
so if D is positive you get 2 results

if D is negative you get 0 results...

i am not allowed to give complete answers


i'll assume it has to equal 0in order to obtain 1 solution
Original post by ubisoft
Make f'(x) = 4 as you know the gradient of the tangent is 4.


By far the easiest method - can be done as mental arithmetic.

c=1

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