If the parabola has vertex at (4, 2) and , then the absolute difference between the extreme values of abc is

Question

If the parabola $y = a x^{2} + b x + c$ has vertex at (4, 2) and $a \in [1, 3]$ , then the absolute difference between the extreme values of abc is

Smart Achievers · Accepted Answer

(3)

$\frac{- b}{2 a} = 4 \Rightarrow b = - 8 a$

$16 a + 4 b + c = 2$

$c = 16 a + 2$

$As a \in [1, 3] \Rightarrow c \in [18, 50]$

Want Us to Email you About Special Offers & Updates?