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Gardner Fisher

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3y ago
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6y ago

If: y = x +c and y = 3 -x -5x^2

Then: x +c = 3 -x -5x^2

Transposing terms: 5x^2 +2x +(c -3) = 0

Using the discriminant formula: 2^2 -4*5*(c -3) = 0 => c = 16/5

Using the quadratic equation formula: 5x^2 -2x +1/5 = 0 => x = -1/5

By substitution: y = 3

Therefore the point of contact is made at: (-1/5, 3)

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Q: What is the point of contact when the tangent line y equals x plus c touches the curve y equals 3 -x -5x squared?
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