Calculus Question

Question

Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the line y = 5x − 5 at (1, 0).

Answer 1

y(x) = ax^2+bx+c

y' = 2ax+b = 5x-5

Therefore a = 2.5 and b = -5

y(x) = 2.5x^2 - 5b + c

y(1) = 2.5 - 5 +c = 0 --> c = 5-2.5 = 2.5

Giving

y = 2.5x^2-5x +2.5

For the equation.