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# Tangents Question watch

1. The parabola passes through point (1,1) and has a tangent with gradient 7 at point (3,3).

Find the values of a, b and c.

So far: I've done

Bit stuck on what to substitute into those equations above.

Thank you!
2. y = ax^2 + bx + c passes through the point (1,1), so when x = 1, y = 1. It also passes through (3,3), so when x = 3, y = 3. Subtract the two resultant equations to get an equation in a and b. Then y' = 2ax + b, and when x = 3, the gradient of the tangent is 7, so y' = 7 - this gives you another equation for a and b. Solve simultaneously.
3. (Original post by generalebriety)
y = ax^2 + bx + c passes through the point (1,1), so when x = 1, y = 1. It also passes through (3,3), so when x = 3, y = 3. Subtract the two resultant equations to get an equation in a and b. Then y' = 2ax + b, and when x = 3, the gradient of the tangent is 7, so y' = 7 - this gives you another equation for a and b. Solve simultaneously.
You're brilliant! Thank you for your help!
4. No problem.

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Updated: February 2, 2010
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