Question

The extreme value of the quadratic function y = -x ^ 2 + 2bx + 16 is 32, then b is
A. 2 or -2
B. 3 or -3
C. 4 or -4
D. 5 or -5
E. 6 or -6

Answer 1

$\displaystyle y=-x^2+2bx+16\\\\y_p=32\\-\frac{D}{4a}=32\\-\frac{b^2-4ac}{4a}=32\\-\frac{(2b)^2-4(-1)(16)}{4(-1)}=32\\\frac{4b^2+64}{4}=32\\b^2+16=32\\b^2=16\\\boxed{\boxed{b=\pm4}}$