Find the parabola with equation y = ax2 + bx whose tangent line at (2, 0) has equation y = 4x − 8.

Question

Find the parabola with equation
y = ax2 + bx
whose tangent line at
(2, 0)
has equation
y = 4x − 8.

 

Answer 1

The parabola has a derivative of 4 at the point (2, 0).

 

y' = 2ax + b

 

2ax + b = 4

 

Plugging in x=2.

 

4a + b = 4                      eq1

 

 

Plug in the point (2, 0) into the parabola.

 

a(2)² + 2b = 0

 

4a + 2b = 0                     eq2

 

 

Solve for "a" and "b" from the system of equations.