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# Tangent to a parabola watch

1. 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.
2. (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?
3. 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.
4. Make f'(x) = 4 as you know the gradient of the tangent is 4.
5. (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?
6. (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
7. (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
8. (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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