Question

Arrange the following quadratic expressions in the ascending order of their extreme values

$A:\frac{11}{3}-{(x-\frac{3}{5})}^2$

$B:x^2-8x+17$

$C:x^2+6x-27$

$D:15+4x-3x^2$

• A. $A,B,C,D$
• B. $B,A,C,D$
• C. $C,B,A,D$
• D. $A,B,D,C$

Answer 1

Answer: (C)

$C,B,A,D$

(A) $\frac{11}{3}-{(x-\frac{3}{5})}^2$ is maximum at $x=\frac{3}{5}$ $=\frac{11}{3}$
(B) Minimum value occurs at $x=4$ , Minimum value $=1$
(C) Extreme value $=\frac{-D^2}{4a}$ $=\frac{-(36+108)}{4}$ $=-36$
(D) Extreme value $=\frac{-D^2}{4a}$ $=\frac{+(16+4\times 15\times 3)}{+4\times 3}$ $=\frac{49}{3}$
(D) > (A) > (B) > (C)