Question

If at x = 1, y = 2x is tangent to the parabola $y=a{x}^2+bx+c$, then respective values of a, b, c possible are

• A. $\frac{1}{2},1,\frac{1}{2}$
• B. $1,\frac{1}{2},\frac{1}{2}$
• C. $\frac{1}{2},\frac{1}{2},1$
• D. $\frac{-1}{2},1,\frac{3}{2}$

Answer 1

The correct option is A $\frac{1}{2},1,\frac{1}{2}$

for x =1, y = a + b + c

Tangent at $(1,a+b+c)is\frac{1}{2}(y+a+b+c)=ax+\frac{b}{2}(x+1)+c$

Comparing with y = 2x, c = a, b = 2(1-a)
Which are true for choice (1) only