Anonymous
asks:
Given that the curve y=ax^2+bx+5 has a of slope of 4 at the point (5,0) find the values if the constants a and b. I know it's a simultaneous equation question but I just don't know how to form the two equations.help please ??

Hello! So the first equation you’d be looking at would be the first derivative of y=ax^2+bx+5, since the first derivative of something is the same as its tangent/slope. You already know the answer to this equation is 4, and you know that this is 4 when x = 5. So: 

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The second equation (the one below the red text) happens when x = 5, and y = 0. This is a point of the function, because it’s where it has a tangent (therefore (5,0) has to be part of the function). So now you have a in terms of b from your first equation, which you then substitute into your new equation (as seen below the red equation). The last part would be to solve the algebra:

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You can prove that your solutions for a and b are correct by finding the value of the tangent at the point (5,0). Since it indeed results in 4, then your solutions are correct.

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