Find the maximum/minimum value of the quadratic expression -4 x2+12 x+9.

Question

Find the maximum/minimum value of the quadratic expression -4 x2+12 x+9. (A) Minimum value is 18 (B) Maximum value is -18 (C) Minimum value is -18 (D) Maximum value is 18

Tardigrade Admin · Accepted Answer

Given: -4 x2+12 x+9 which is in the form of a x2+b x+c, where a=-4< 0. ∴ text Maximum value =(4 a c-b2/4 a) =(4(-3)(9)-(12)2/4(-3))=(4(4)(9)+144/4(4))=18

Q. Find the maximum/minimum value of the quadratic expression $- 4 x^{2} + 12 x + 9$ .

Minimum value is 18

Maximum value is -18

Minimum value is -18

Maximum value is 18

Given: $- 4 x^{2} + 12 x + 9$ which is in the form of $a x^{2} + b x + c$ ,
where $a = - 4 < 0$ .
$∴ Maximum value = \frac{4 a c - b ^{2}}{4 a}$
$= \frac{4 ( - 3 ) ( 9 ) - ( 12 ) ^{2}}{4 ( - 3 )} = \frac{4 ( 4 ) ( 9 ) + 144}{4 ( 4 )} = 18$

Q. Find the maximum/minimum value of the quadratic expression −4x2+12x+9.