Finding the equation for the parabola

  • Thread starter Burnstreak
  • Start date
1. The problem statement, all variables and given/known data
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)


2. Relevant 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.


3. 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.
 

HallsofIvy

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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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