Find the parabola with equation y = ax2 + bx whose tangent line at (1, 0) has equation y = 2x − 2

Answer 1

Slope of tangent line = 2 and slope of tangent line = y' evaluated at x = 1

y' = 2ax + b So, when x = 1, we have y' = 2a + b

Therefore, 2a + b = 2. Also, the point (1,0) is on the curve y = ax² + bx. So, a + b = 0

Solve the system of equations:

2a + b = 2

a + b = 0