Finding the equation for the parabola

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Homework Help Overview

The discussion revolves around finding the equation of a parabola in the form y=ax^2+bx, given a tangent line at a specific point P(2,2) with the equation y=5x-8. Participants are exploring the relationships between the parabola and its tangent line.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to derive the coefficients a and b by using the derivative of the parabola and equating it to the slope of the tangent line. Some participants question the clarity of the original poster's calculations and suggest providing more detail on their process. Others note the importance of the point P(2,2) in forming additional equations.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's approach and encouraging them to clarify their calculations. There is recognition of the need for multiple equations to solve for the unknowns a and b, but no consensus has been reached yet.

Contextual Notes

Participants are working under the constraints of the problem as stated, with specific values for the tangent line and point P. There is an emphasis on the need for clear communication of the steps taken in the calculations.

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Homework Statement


Find the parabola of the form y=ax^2+bx, whose tangent at given point P has equation y.
y=5x-8
P=(2,2)


Homework Equations


I guess the equations involved would be the equation for the parabola: y=ax^2+bx, and the y-y1=m(x-x1) for the slope.


The Attempt at a Solution


Using the parabola equation, I found a general derivative and then input the x and y' values in order to try and find a and b, but I was unable to solve for either.
 
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Why in the world do you tell us that you did all those things without showing us exactly what you got when you did it? We can't tell where you went wrong if you don't show us what you did!

You know, I hope, that the line y= 5x- 8 has slope 5 and if x= 2, y= 2.
 
Okay, well in order to find the slope, I took the derivative of the parabola equation and got 2ax+b for the derivative. I sent it equal to 5 since that is the slope and put in 2 for x since it is given getting 5=4a+b. This is where I got lost. I didn't know what to do once I got to this point.
 
You also know that when x = 2, y = 2. This gives you another equation.
 

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